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contract UniswapV3Pool is IUniswapV3Pool, NoDelegateCall {

using LowGasSafeMath for uint256;

using LowGasSafeMath for int256;

using SafeCast for uint256;

using SafeCast for int256;

using Tick for mapping(int24 => Tick.Info);

using TickBitmap for mapping(int16 => uint256);

using Position for mapping(bytes32 => Position.Info);

using Position for Position.Info;

using Oracle for Oracle.Observation[65535];

/// @inheritdoc IUniswapV3PoolImmutables

address public immutable override factory;

/// @inheritdoc IUniswapV3PoolImmutables

address public immutable override token0;

/// @inheritdoc IUniswapV3PoolImmutables

address public immutable override token1;

/// @inheritdoc IUniswapV3PoolImmutables

uint24 public immutable override fee;

/// @inheritdoc IUniswapV3PoolImmutables

int24 public immutable override tickSpacing;

/// @inheritdoc IUniswapV3PoolImmutables

uint128 public immutable override maxLiquidityPerTick;

struct Slot0 {

// the current price

uint160 sqrtPriceX96;

// the current tick

int24 tick;

// the most-recently updated index of the observations array

uint16 observationIndex;

// the current maximum number of observations that are being stored

uint16 observationCardinality;

// the next maximum number of observations to store, triggered in observations.write

uint16 observationCardinalityNext;

// the current protocol fee as a percentage of the swap fee taken on withdrawal

// represented as an integer denominator (1/x)%

uint8 feeProtocol;

// whether the pool is locked

bool unlocked;

}

/// @inheritdoc IUniswapV3PoolState

Slot0 public override slot0;

/// @inheritdoc IUniswapV3PoolState

uint256 public override feeGrowthGlobal0X128;

/// @inheritdoc IUniswapV3PoolState

uint256 public override feeGrowthGlobal1X128;

// accumulated protocol fees in token0/token1 units

struct ProtocolFees {

uint128 token0;

uint128 token1;

}

/// @inheritdoc IUniswapV3PoolState

ProtocolFees public override protocolFees;

/// @inheritdoc IUniswapV3PoolState

uint128 public override liquidity;

/// @inheritdoc IUniswapV3PoolState

mapping(int24 => Tick.Info) public override ticks;

/// @inheritdoc IUniswapV3PoolState

mapping(int16 => uint256) public override tickBitmap;

/// @inheritdoc IUniswapV3PoolState

mapping(bytes32 => Position.Info) public override positions;

/// @inheritdoc IUniswapV3PoolState

Oracle.Observation[65535] public override observations;

/// @dev Mutually exclusive reentrancy protection into the pool to/from a method. This method also prevents entrance

/// to a function before the pool is initialized. The reentrancy guard is required throughout the contract because

/// we use balance checks to determine the payment status of interactions such as mint, swap and flash.

modifier lock() {

require(slot0.unlocked, 'LOK');

slot0.unlocked = false;

slot0.unlocked = true;

}

/// @dev Prevents calling a function from anyone except the address returned by IUniswapV3Factory#owner()

modifier onlyFactoryOwner() {

require(msg.sender == IUniswapV3Factory(factory).owner());

}

constructor() {

int24 _tickSpacing;

(factory, token0, token1, fee, _tickSpacing) = IUniswapV3PoolDeployer(msg.sender).parameters();

tickSpacing = _tickSpacing;

maxLiquidityPerTick = Tick.tickSpacingToMaxLiquidityPerTick(_tickSpacing);

}

/// @dev Common checks for valid tick inputs.

function checkTicks(int24 tickLower, int24 tickUpper) private pure {

require(tickLower < tickUpper, 'TLU');

require(tickLower >= TickMath.MIN_TICK, 'TLM');

require(tickUpper <= TickMath.MAX_TICK, 'TUM');

}

/// @dev Returns the block timestamp truncated to 32 bits, i.e. mod 2**32. This method is overridden in tests.

function _blockTimestamp() internal view virtual returns (uint32) {

return uint32(block.timestamp); // truncation is desired

}

/// @dev Get the pool's balance of token0

/// @dev This function is gas optimized to avoid a redundant extcodesize check in addition to the returndatasize

/// check

function balance0() private view returns (uint256) {

(bool success, bytes memory data) =

token0.staticcall(abi.encodeWithSelector(IERC20Minimal.balanceOf.selector, address(this)));

require(success && data.length >= 32);

return abi.decode(data, (uint256));

}

/// @dev Get the pool's balance of token1

/// @dev This function is gas optimized to avoid a redundant extcodesize check in addition to the returndatasize

/// check

function balance1() private view returns (uint256) {

(bool success, bytes memory data) =

token1.staticcall(abi.encodeWithSelector(IERC20Minimal.balanceOf.selector, address(this)));

require(success && data.length >= 32);

return abi.decode(data, (uint256));

}

/// @inheritdoc IUniswapV3PoolDerivedState

function snapshotCumulativesInside(int24 tickLower, int24 tickUpper)

external

view

override

noDelegateCall

returns (

int56 tickCumulativeInside,

uint160 secondsPerLiquidityInsideX128,

uint32 secondsInside

)

{

checkTicks(tickLower, tickUpper);

int56 tickCumulativeLower;

int56 tickCumulativeUpper;

uint160 secondsPerLiquidityOutsideLowerX128;

uint160 secondsPerLiquidityOutsideUpperX128;

uint32 secondsOutsideLower;

uint32 secondsOutsideUpper;

{

Tick.Info storage lower = ticks[tickLower];

Tick.Info storage upper = ticks[tickUpper];

bool initializedLower;

(tickCumulativeLower, secondsPerLiquidityOutsideLowerX128, secondsOutsideLower, initializedLower) = (

lower.tickCumulativeOutside,

lower.secondsPerLiquidityOutsideX128,

lower.secondsOutside,

lower.initialized

);

require(initializedLower);

bool initializedUpper;

(tickCumulativeUpper, secondsPerLiquidityOutsideUpperX128, secondsOutsideUpper, initializedUpper) = (

upper.tickCumulativeOutside,

upper.secondsPerLiquidityOutsideX128,

upper.secondsOutside,

upper.initialized

);

require(initializedUpper);

}

Slot0 memory _slot0 = slot0;

if (_slot0.tick < tickLower) {

return (

tickCumulativeLower - tickCumulativeUpper,

secondsPerLiquidityOutsideLowerX128 - secondsPerLiquidityOutsideUpperX128,

secondsOutsideLower - secondsOutsideUpper

);

} else if (_slot0.tick < tickUpper) {

uint32 time = _blockTimestamp();

(int56 tickCumulative, uint160 secondsPerLiquidityCumulativeX128) =

observations.observeSingle(

time,

_slot0.tick,

_slot0.observationIndex,

liquidity,

_slot0.observationCardinality

);

return (

tickCumulative - tickCumulativeLower - tickCumulativeUpper,

secondsPerLiquidityCumulativeX128 -

secondsPerLiquidityOutsideLowerX128 -

secondsPerLiquidityOutsideUpperX128,

time - secondsOutsideLower - secondsOutsideUpper

);

} else {

return (

tickCumulativeUpper - tickCumulativeLower,

secondsPerLiquidityOutsideUpperX128 - secondsPerLiquidityOutsideLowerX128,

secondsOutsideUpper - secondsOutsideLower

);

}

/// @inheritdoc IUniswapV3PoolDerivedState

function observe(uint32[] calldata secondsAgos)

external

view

override

noDelegateCall

returns (int56[] memory tickCumulatives, uint160[] memory secondsPerLiquidityCumulativeX128s)

{

return

observations.observe(

_blockTimestamp(),

secondsAgos,

slot0.tick,

slot0.observationIndex,

liquidity,

slot0.observationCardinality

);

}

/// @inheritdoc IUniswapV3PoolActions

function increaseObservationCardinalityNext(uint16 observationCardinalityNext)

external

override

lock

noDelegateCall

{

uint16 observationCardinalityNextOld = slot0.observationCardinalityNext; // for the event

uint16 observationCardinalityNextNew =

observations.grow(observationCardinalityNextOld, observationCardinalityNext);

slot0.observationCardinalityNext = observationCardinalityNextNew;

if (observationCardinalityNextOld != observationCardinalityNextNew)

emit IncreaseObservationCardinalityNext(observationCardinalityNextOld, observationCardinalityNextNew);

}

/// @inheritdoc IUniswapV3PoolActions

/// @dev not locked because it initializes unlocked

function initialize(uint160 sqrtPriceX96) external override {

require(slot0.sqrtPriceX96 == 0, 'AI');

int24 tick = TickMath.getTickAtSqrtRatio(sqrtPriceX96);

(uint16 cardinality, uint16 cardinalityNext) = observations.initialize(_blockTimestamp());

slot0 = Slot0({

sqrtPriceX96: sqrtPriceX96,

tick: tick,

observationIndex: 0,

observationCardinality: cardinality,

observationCardinalityNext: cardinalityNext,

feeProtocol: 0,

unlocked: true

});

emit Initialize(sqrtPriceX96, tick);

}

struct ModifyPositionParams {

// the address that owns the position

address owner;

// the lower and upper tick of the position

int24 tickLower;

int24 tickUpper;

// any change in liquidity

int128 liquidityDelta;

}

/// @dev Effect some changes to a position

/// @param params the position details and the change to the position's liquidity to effect

/// @return position a storage pointer referencing the position with the given owner and tick range

/// @return amount0 the amount of token0 owed to the pool, negative if the pool should pay the recipient

/// @return amount1 the amount of token1 owed to the pool, negative if the pool should pay the recipient

function _modifyPosition(ModifyPositionParams memory params)

private

noDelegateCall

returns (

Position.Info storage position,

int256 amount0,

int256 amount1

)

{

checkTicks(params.tickLower, params.tickUpper);

Slot0 memory _slot0 = slot0; // SLOAD for gas optimization

position = _updatePosition(

params.owner,

params.tickLower,

params.tickUpper,

params.liquidityDelta,

_slot0.tick

);

if (params.liquidityDelta != 0) {

if (_slot0.tick < params.tickLower) {

// current tick is below the passed range; liquidity can only become in range by crossing from left to

// right, when we'll need _more_ token0 (it's becoming more valuable) so user must provide it

amount0 = SqrtPriceMath.getAmount0Delta(

TickMath.getSqrtRatioAtTick(params.tickLower),

TickMath.getSqrtRatioAtTick(params.tickUpper),

params.liquidityDelta

);

} else if (_slot0.tick < params.tickUpper) {

// current tick is inside the passed range

uint128 liquidityBefore = liquidity; // SLOAD for gas optimization

// write an oracle entry

(slot0.observationIndex, slot0.observationCardinality) = observations.write(

_slot0.observationIndex,

_blockTimestamp(),

_slot0.tick,

liquidityBefore,

_slot0.observationCardinality,

_slot0.observationCardinalityNext

);

amount0 = SqrtPriceMath.getAmount0Delta(

_slot0.sqrtPriceX96,

TickMath.getSqrtRatioAtTick(params.tickUpper),

params.liquidityDelta

);

amount1 = SqrtPriceMath.getAmount1Delta(

TickMath.getSqrtRatioAtTick(params.tickLower),

_slot0.sqrtPriceX96,

params.liquidityDelta

);

liquidity = LiquidityMath.addDelta(liquidityBefore, params.liquidityDelta);

} else {

// current tick is above the passed range; liquidity can only become in range by crossing from right to

// left, when we'll need _more_ token1 (it's becoming more valuable) so user must provide it

amount1 = SqrtPriceMath.getAmount1Delta(

TickMath.getSqrtRatioAtTick(params.tickLower),

TickMath.getSqrtRatioAtTick(params.tickUpper),

params.liquidityDelta

);

}

/// @dev Gets and updates a position with the given liquidity delta

/// @param owner the owner of the position

/// @param tickLower the lower tick of the position's tick range

/// @param tickUpper the upper tick of the position's tick range

/// @param tick the current tick, passed to avoid sloads

function _updatePosition(

address owner,

int24 tickLower,

int24 tickUpper,

int128 liquidityDelta,

int24 tick

) private returns (Position.Info storage position) {

position = positions.get(owner, tickLower, tickUpper);

uint256 _feeGrowthGlobal0X128 = feeGrowthGlobal0X128; // SLOAD for gas optimization

uint256 _feeGrowthGlobal1X128 = feeGrowthGlobal1X128; // SLOAD for gas optimization

// if we need to update the ticks, do it

bool flippedLower;

bool flippedUpper;

if (liquidityDelta != 0) {

uint32 time = _blockTimestamp();

(int56 tickCumulative, uint160 secondsPerLiquidityCumulativeX128) =

observations.observeSingle(

time,

slot0.tick,

slot0.observationIndex,

liquidity,

slot0.observationCardinality

);

flippedLower = ticks.update(

tickLower,

tick,

liquidityDelta,

_feeGrowthGlobal0X128,

_feeGrowthGlobal1X128,

secondsPerLiquidityCumulativeX128,

tickCumulative,

time,

false,

maxLiquidityPerTick

);

flippedUpper = ticks.update(

tickUpper,

tick,

liquidityDelta,

_feeGrowthGlobal0X128,

_feeGrowthGlobal1X128,

secondsPerLiquidityCumulativeX128,

tickCumulative,

time,

true,

maxLiquidityPerTick

);

if (flippedLower) {

tickBitmap.flipTick(tickLower, tickSpacing);

}

if (flippedUpper) {

tickBitmap.flipTick(tickUpper, tickSpacing);

}

(uint256 feeGrowthInside0X128, uint256 feeGrowthInside1X128) =

ticks.getFeeGrowthInside(tickLower, tickUpper, tick, _feeGrowthGlobal0X128, _feeGrowthGlobal1X128);

position.update(liquidityDelta, feeGrowthInside0X128, feeGrowthInside1X128);

// clear any tick data that is no longer needed

if (liquidityDelta < 0) {

if (flippedLower) {

ticks.clear(tickLower);

}

if (flippedUpper) {

ticks.clear(tickUpper);

}

/// @inheritdoc IUniswapV3PoolActions

/// @dev noDelegateCall is applied indirectly via _modifyPosition

function mint(

address recipient,

int24 tickLower,

int24 tickUpper,

uint128 amount,

bytes calldata data

) external override lock returns (uint256 amount0, uint256 amount1) {

require(amount > 0);

(, int256 amount0Int, int256 amount1Int) =

_modifyPosition(

ModifyPositionParams({

owner: recipient,

tickLower: tickLower,

tickUpper: tickUpper,

liquidityDelta: int256(amount).toInt128()

})

);

amount0 = uint256(amount0Int);

amount1 = uint256(amount1Int);

uint256 balance0Before;

uint256 balance1Before;

if (amount0 > 0) balance0Before = balance0();

if (amount1 > 0) balance1Before = balance1();

IUniswapV3MintCallback(msg.sender).uniswapV3MintCallback(amount0, amount1, data);

if (amount0 > 0) require(balance0Before.add(amount0) <= balance0(), 'M0');

if (amount1 > 0) require(balance1Before.add(amount1) <= balance1(), 'M1');

emit Mint(msg.sender, recipient, tickLower, tickUpper, amount, amount0, amount1);

}

/// @inheritdoc IUniswapV3PoolActions

function collect(

address recipient,

int24 tickLower,

int24 tickUpper,

uint128 amount0Requested,

uint128 amount1Requested

) external override lock returns (uint128 amount0, uint128 amount1) {

// we don't need to checkTicks here, because invalid positions will never have non-zero tokensOwed{0,1}

Position.Info storage position = positions.get(msg.sender, tickLower, tickUpper);

amount0 = amount0Requested > position.tokensOwed0 ? position.tokensOwed0 : amount0Requested;

amount1 = amount1Requested > position.tokensOwed1 ? position.tokensOwed1 : amount1Requested;

if (amount0 > 0) {

position.tokensOwed0 -= amount0;

TransferHelper.safeTransfer(token0, recipient, amount0);

}

if (amount1 > 0) {

position.tokensOwed1 -= amount1;

TransferHelper.safeTransfer(token1, recipient, amount1);

}

emit Collect(msg.sender, recipient, tickLower, tickUpper, amount0, amount1);

}

/// @inheritdoc IUniswapV3PoolActions

/// @dev noDelegateCall is applied indirectly via _modifyPosition

function burn(

int24 tickLower,

int24 tickUpper,

uint128 amount

) external override lock returns (uint256 amount0, uint256 amount1) {

(Position.Info storage position, int256 amount0Int, int256 amount1Int) =

_modifyPosition(

ModifyPositionParams({

owner: msg.sender,

tickLower: tickLower,

tickUpper: tickUpper,

liquidityDelta: -int256(amount).toInt128()

})

);

amount0 = uint256(-amount0Int);

amount1 = uint256(-amount1Int);

if (amount0 > 0 || amount1 > 0) {

(position.tokensOwed0, position.tokensOwed1) = (

position.tokensOwed0 + uint128(amount0),

position.tokensOwed1 + uint128(amount1)

);

}

emit Burn(msg.sender, tickLower, tickUpper, amount, amount0, amount1);

}

struct SwapCache {

// the protocol fee for the input token

uint8 feeProtocol;

// liquidity at the beginning of the swap

uint128 liquidityStart;

// the timestamp of the current block

uint32 blockTimestamp;

// the current value of the tick accumulator, computed only if we cross an initialized tick

int56 tickCumulative;

// the current value of seconds per liquidity accumulator, computed only if we cross an initialized tick

uint160 secondsPerLiquidityCumulativeX128;

// whether we've computed and cached the above two accumulators

bool computedLatestObservation;

}

// the top level state of the swap, the results of which are recorded in storage at the end

struct SwapState {

// the amount remaining to be swapped in/out of the input/output asset

int256 amountSpecifiedRemaining;

// the amount already swapped out/in of the output/input asset

int256 amountCalculated;

// current sqrt(price)

uint160 sqrtPriceX96;

// the tick associated with the current price

int24 tick;

// the global fee growth of the input token

uint256 feeGrowthGlobalX128;

// amount of input token paid as protocol fee

uint128 protocolFee;

// the current liquidity in range

uint128 liquidity;

}

struct StepComputations {

// the price at the beginning of the step

uint160 sqrtPriceStartX96;

// the next tick to swap to from the current tick in the swap direction

int24 tickNext;

// whether tickNext is initialized or not

bool initialized;

// sqrt(price) for the next tick (1/0)

uint160 sqrtPriceNextX96;

// how much is being swapped in in this step

uint256 amountIn;

// how much is being swapped out

uint256 amountOut;

// how much fee is being paid in

uint256 feeAmount;

}

/// @inheritdoc IUniswapV3PoolActions

function swap(

address recipient,

bool zeroForOne,

int256 amountSpecified,

uint160 sqrtPriceLimitX96,

bytes calldata data

) external override noDelegateCall returns (int256 amount0, int256 amount1) {

require(amountSpecified != 0, 'AS');

Slot0 memory slot0Start = slot0;

require(slot0Start.unlocked, 'LOK');

require(

zeroForOne

? sqrtPriceLimitX96 < slot0Start.sqrtPriceX96 && sqrtPriceLimitX96 > TickMath.MIN_SQRT_RATIO

: sqrtPriceLimitX96 > slot0Start.sqrtPriceX96 && sqrtPriceLimitX96 < TickMath.MAX_SQRT_RATIO,

'SPL'

);

slot0.unlocked = false;

SwapCache memory cache =

SwapCache({

liquidityStart: liquidity,

blockTimestamp: _blockTimestamp(),

feeProtocol: zeroForOne ? (slot0Start.feeProtocol % 16) : (slot0Start.feeProtocol >> 4),

secondsPerLiquidityCumulativeX128: 0,

tickCumulative: 0,

computedLatestObservation: false

});

bool exactInput = amountSpecified > 0;

SwapState memory state =

SwapState({

amountSpecifiedRemaining: amountSpecified,

amountCalculated: 0,

sqrtPriceX96: slot0Start.sqrtPriceX96,

tick: slot0Start.tick,

feeGrowthGlobalX128: zeroForOne ? feeGrowthGlobal0X128 : feeGrowthGlobal1X128,

protocolFee: 0,

liquidity: cache.liquidityStart

});

// continue swapping as long as we haven't used the entire input/output and haven't reached the price limit

while (state.amountSpecifiedRemaining != 0 && state.sqrtPriceX96 != sqrtPriceLimitX96) {

StepComputations memory step;

step.sqrtPriceStartX96 = state.sqrtPriceX96;

(step.tickNext, step.initialized) = tickBitmap.nextInitializedTickWithinOneWord(

state.tick,

tickSpacing,

zeroForOne

);

// ensure that we do not overshoot the min/max tick, as the tick bitmap is not aware of these bounds

if (step.tickNext < TickMath.MIN_TICK) {

step.tickNext = TickMath.MIN_TICK;

} else if (step.tickNext > TickMath.MAX_TICK) {

step.tickNext = TickMath.MAX_TICK;

}

// get the price for the next tick

step.sqrtPriceNextX96 = TickMath.getSqrtRatioAtTick(step.tickNext);

// compute values to swap to the target tick, price limit, or point where input/output amount is exhausted

(state.sqrtPriceX96, step.amountIn, step.amountOut, step.feeAmount) = SwapMath.computeSwapStep(

state.sqrtPriceX96,

(zeroForOne ? step.sqrtPriceNextX96 < sqrtPriceLimitX96 : step.sqrtPriceNextX96 > sqrtPriceLimitX96)

? sqrtPriceLimitX96

: step.sqrtPriceNe

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contract UniswapV3Pool is IUniswapV3Pool, NoDelegateCall {
    using LowGasSafeMath for uint256;
    using LowGasSafeMath for int256;
    using SafeCast for uint256;
    using SafeCast for int256;
    using Tick for mapping(int24 => Tick.Info);
    using TickBitmap for mapping(int16 => uint256);
    using Position for mapping(bytes32 => Position.Info);
    using Position for Position.Info;
    using Oracle for Oracle.Observation[65535];

    /// @inheritdoc IUniswapV3PoolImmutables
    address public immutable override factory;
    /// @inheritdoc IUniswapV3PoolImmutables
    address public immutable override token0;
    /// @inheritdoc IUniswapV3PoolImmutables
    address public immutable override token1;
    /// @inheritdoc IUniswapV3PoolImmutables
    uint24 public immutable override fee;

    /// @inheritdoc IUniswapV3PoolImmutables
    int24 public immutable override tickSpacing;

    /// @inheritdoc IUniswapV3PoolImmutables
    uint128 public immutable override maxLiquidityPerTick;

    struct Slot0 {
        // the current price
        uint160 sqrtPriceX96;
        // the current tick
        int24 tick;
        // the most-recently updated index of the observations array
        uint16 observationIndex;
        // the current maximum number of observations that are being stored
        uint16 observationCardinality;
        // the next maximum number of observations to store, triggered in observations.write
        uint16 observationCardinalityNext;
        // the current protocol fee as a percentage of the swap fee taken on withdrawal
        // represented as an integer denominator (1/x)%
        uint8 feeProtocol;
        // whether the pool is locked
        bool unlocked;
    }
    /// @inheritdoc IUniswapV3PoolState
    Slot0 public override slot0;

    /// @inheritdoc IUniswapV3PoolState
    uint256 public override feeGrowthGlobal0X128;
    /// @inheritdoc IUniswapV3PoolState
    uint256 public override feeGrowthGlobal1X128;

    // accumulated protocol fees in token0/token1 units
    struct ProtocolFees {
        uint128 token0;
        uint128 token1;
    }
    /// @inheritdoc IUniswapV3PoolState
    ProtocolFees public override protocolFees;

    /// @inheritdoc IUniswapV3PoolState
    uint128 public override liquidity;

    /// @inheritdoc IUniswapV3PoolState
    mapping(int24 => Tick.Info) public override ticks;
    /// @inheritdoc IUniswapV3PoolState
    mapping(int16 => uint256) public override tickBitmap;
    /// @inheritdoc IUniswapV3PoolState
    mapping(bytes32 => Position.Info) public override positions;
    /// @inheritdoc IUniswapV3PoolState
    Oracle.Observation[65535] public override observations;

    /// @dev Mutually exclusive reentrancy protection into the pool to/from a method. This method also prevents entrance
    /// to a function before the pool is initialized. The reentrancy guard is required throughout the contract because
    /// we use balance checks to determine the payment status of interactions such as mint, swap and flash.
    modifier lock() {
        require(slot0.unlocked, 'LOK');
        slot0.unlocked = false;
        _;
        slot0.unlocked = true;
    }

    /// @dev Prevents calling a function from anyone except the address returned by IUniswapV3Factory#owner()
    modifier onlyFactoryOwner() {
        require(msg.sender == IUniswapV3Factory(factory).owner());
        _;
    }

    constructor() {
        int24 _tickSpacing;
        (factory, token0, token1, fee, _tickSpacing) = IUniswapV3PoolDeployer(msg.sender).parameters();
        tickSpacing = _tickSpacing;

        maxLiquidityPerTick = Tick.tickSpacingToMaxLiquidityPerTick(_tickSpacing);
    }

    /// @dev Common checks for valid tick inputs.
    function checkTicks(int24 tickLower, int24 tickUpper) private pure {
        require(tickLower < tickUpper, 'TLU');
        require(tickLower >= TickMath.MIN_TICK, 'TLM');
        require(tickUpper <= TickMath.MAX_TICK, 'TUM');
    }

    /// @dev Returns the block timestamp truncated to 32 bits, i.e. mod 2**32. This method is overridden in tests.
    function _blockTimestamp() internal view virtual returns (uint32) {
        return uint32(block.timestamp); // truncation is desired
    }

    /// @dev Get the pool's balance of token0
    /// @dev This function is gas optimized to avoid a redundant extcodesize check in addition to the returndatasize
    /// check
    function balance0() private view returns (uint256) {
        (bool success, bytes memory data) =
            token0.staticcall(abi.encodeWithSelector(IERC20Minimal.balanceOf.selector, address(this)));
        require(success && data.length >= 32);
        return abi.decode(data, (uint256));
    }

    /// @dev Get the pool's balance of token1
    /// @dev This function is gas optimized to avoid a redundant extcodesize check in addition to the returndatasize
    /// check
    function balance1() private view returns (uint256) {
        (bool success, bytes memory data) =
            token1.staticcall(abi.encodeWithSelector(IERC20Minimal.balanceOf.selector, address(this)));
        require(success && data.length >= 32);
        return abi.decode(data, (uint256));
    }

    /// @inheritdoc IUniswapV3PoolDerivedState
    function snapshotCumulativesInside(int24 tickLower, int24 tickUpper)
        external
        view
        override
        noDelegateCall
        returns (
            int56 tickCumulativeInside,
            uint160 secondsPerLiquidityInsideX128,
            uint32 secondsInside
        )
    {
        checkTicks(tickLower, tickUpper);

        int56 tickCumulativeLower;
        int56 tickCumulativeUpper;
        uint160 secondsPerLiquidityOutsideLowerX128;
        uint160 secondsPerLiquidityOutsideUpperX128;
        uint32 secondsOutsideLower;
        uint32 secondsOutsideUpper;

        {
            Tick.Info storage lower = ticks[tickLower];
            Tick.Info storage upper = ticks[tickUpper];
            bool initializedLower;
            (tickCumulativeLower, secondsPerLiquidityOutsideLowerX128, secondsOutsideLower, initializedLower) = (
                lower.tickCumulativeOutside,
                lower.secondsPerLiquidityOutsideX128,
                lower.secondsOutside,
                lower.initialized
            );
            require(initializedLower);

            bool initializedUpper;
            (tickCumulativeUpper, secondsPerLiquidityOutsideUpperX128, secondsOutsideUpper, initializedUpper) = (
                upper.tickCumulativeOutside,
                upper.secondsPerLiquidityOutsideX128,
                upper.secondsOutside,
                upper.initialized
            );
            require(initializedUpper);
        }

        Slot0 memory _slot0 = slot0;

        if (_slot0.tick < tickLower) {
            return (
                tickCumulativeLower - tickCumulativeUpper,
                secondsPerLiquidityOutsideLowerX128 - secondsPerLiquidityOutsideUpperX128,
                secondsOutsideLower - secondsOutsideUpper
            );
        } else if (_slot0.tick < tickUpper) {
            uint32 time = _blockTimestamp();
            (int56 tickCumulative, uint160 secondsPerLiquidityCumulativeX128) =
                observations.observeSingle(
                    time,
                    0,
                    _slot0.tick,
                    _slot0.observationIndex,
                    liquidity,
                    _slot0.observationCardinality
                );
            return (
                tickCumulative - tickCumulativeLower - tickCumulativeUpper,
                secondsPerLiquidityCumulativeX128 -
                    secondsPerLiquidityOutsideLowerX128 -
                    secondsPerLiquidityOutsideUpperX128,
                time - secondsOutsideLower - secondsOutsideUpper
            );
        } else {
            return (
                tickCumulativeUpper - tickCumulativeLower,
                secondsPerLiquidityOutsideUpperX128 - secondsPerLiquidityOutsideLowerX128,
                secondsOutsideUpper - secondsOutsideLower
            );
        }
    }

    /// @inheritdoc IUniswapV3PoolDerivedState
    function observe(uint32[] calldata secondsAgos)
        external
        view
        override
        noDelegateCall
        returns (int56[] memory tickCumulatives, uint160[] memory secondsPerLiquidityCumulativeX128s)
    {
        return
            observations.observe(
                _blockTimestamp(),
                secondsAgos,
                slot0.tick,
                slot0.observationIndex,
                liquidity,
                slot0.observationCardinality
            );
    }

    /// @inheritdoc IUniswapV3PoolActions
    function increaseObservationCardinalityNext(uint16 observationCardinalityNext)
        external
        override
        lock
        noDelegateCall
    {
        uint16 observationCardinalityNextOld = slot0.observationCardinalityNext; // for the event
        uint16 observationCardinalityNextNew =
            observations.grow(observationCardinalityNextOld, observationCardinalityNext);
        slot0.observationCardinalityNext = observationCardinalityNextNew;
        if (observationCardinalityNextOld != observationCardinalityNextNew)
            emit IncreaseObservationCardinalityNext(observationCardinalityNextOld, observationCardinalityNextNew);
    }

    /// @inheritdoc IUniswapV3PoolActions
    /// @dev not locked because it initializes unlocked
    function initialize(uint160 sqrtPriceX96) external override {
        require(slot0.sqrtPriceX96 == 0, 'AI');

        int24 tick = TickMath.getTickAtSqrtRatio(sqrtPriceX96);

        (uint16 cardinality, uint16 cardinalityNext) = observations.initialize(_blockTimestamp());

        slot0 = Slot0({
            sqrtPriceX96: sqrtPriceX96,
            tick: tick,
            observationIndex: 0,
            observationCardinality: cardinality,
            observationCardinalityNext: cardinalityNext,
            feeProtocol: 0,
            unlocked: true
        });

        emit Initialize(sqrtPriceX96, tick);
    }

    struct ModifyPositionParams {
        // the address that owns the position
        address owner;
        // the lower and upper tick of the position
        int24 tickLower;
        int24 tickUpper;
        // any change in liquidity
        int128 liquidityDelta;
    }

    /// @dev Effect some changes to a position
    /// @param params the position details and the change to the position's liquidity to effect
    /// @return position a storage pointer referencing the position with the given owner and tick range
    /// @return amount0 the amount of token0 owed to the pool, negative if the pool should pay the recipient
    /// @return amount1 the amount of token1 owed to the pool, negative if the pool should pay the recipient
    function _modifyPosition(ModifyPositionParams memory params)
        private
        noDelegateCall
        returns (
            Position.Info storage position,
            int256 amount0,
            int256 amount1
        )
    {
        checkTicks(params.tickLower, params.tickUpper);

        Slot0 memory _slot0 = slot0; // SLOAD for gas optimization

        position = _updatePosition(
            params.owner,
            params.tickLower,
            params.tickUpper,
            params.liquidityDelta,
            _slot0.tick
        );

        if (params.liquidityDelta != 0) {
            if (_slot0.tick < params.tickLower) {
                // current tick is below the passed range; liquidity can only become in range by crossing from left to
                // right, when we'll need _more_ token0 (it's becoming more valuable) so user must provide it
                amount0 = SqrtPriceMath.getAmount0Delta(
                    TickMath.getSqrtRatioAtTick(params.tickLower),
                    TickMath.getSqrtRatioAtTick(params.tickUpper),
                    params.liquidityDelta
                );
            } else if (_slot0.tick < params.tickUpper) {
                // current tick is inside the passed range
                uint128 liquidityBefore = liquidity; // SLOAD for gas optimization

                // write an oracle entry
                (slot0.observationIndex, slot0.observationCardinality) = observations.write(
                    _slot0.observationIndex,
                    _blockTimestamp(),
                    _slot0.tick,
                    liquidityBefore,
                    _slot0.observationCardinality,
                    _slot0.observationCardinalityNext
                );

                amount0 = SqrtPriceMath.getAmount0Delta(
                    _slot0.sqrtPriceX96,
                    TickMath.getSqrtRatioAtTick(params.tickUpper),
                    params.liquidityDelta
                );
                amount1 = SqrtPriceMath.getAmount1Delta(
                    TickMath.getSqrtRatioAtTick(params.tickLower),
                    _slot0.sqrtPriceX96,
                    params.liquidityDelta
                );

                liquidity = LiquidityMath.addDelta(liquidityBefore, params.liquidityDelta);
            } else {
                // current tick is above the passed range; liquidity can only become in range by crossing from right to
                // left, when we'll need _more_ token1 (it's becoming more valuable) so user must provide it
                amount1 = SqrtPriceMath.getAmount1Delta(
                    TickMath.getSqrtRatioAtTick(params.tickLower),
                    TickMath.getSqrtRatioAtTick(params.tickUpper),
                    params.liquidityDelta
                );
            }
        }
    }

    /// @dev Gets and updates a position with the given liquidity delta
    /// @param owner the owner of the position
    /// @param tickLower the lower tick of the position's tick range
    /// @param tickUpper the upper tick of the position's tick range
    /// @param tick the current tick, passed to avoid sloads
    function _updatePosition(
        address owner,
        int24 tickLower,
        int24 tickUpper,
        int128 liquidityDelta,
        int24 tick
    ) private returns (Position.Info storage position) {
        position = positions.get(owner, tickLower, tickUpper);

        uint256 _feeGrowthGlobal0X128 = feeGrowthGlobal0X128; // SLOAD for gas optimization
        uint256 _feeGrowthGlobal1X128 = feeGrowthGlobal1X128; // SLOAD for gas optimization

        // if we need to update the ticks, do it
        bool flippedLower;
        bool flippedUpper;
        if (liquidityDelta != 0) {
            uint32 time = _blockTimestamp();
            (int56 tickCumulative, uint160 secondsPerLiquidityCumulativeX128) =
                observations.observeSingle(
                    time,
                    0,
                    slot0.tick,
                    slot0.observationIndex,
                    liquidity,
                    slot0.observationCardinality
                );

            flippedLower = ticks.update(
                tickLower,
                tick,
                liquidityDelta,
                _feeGrowthGlobal0X128,
                _feeGrowthGlobal1X128,
                secondsPerLiquidityCumulativeX128,
                tickCumulative,
                time,
                false,
                maxLiquidityPerTick
            );
            flippedUpper = ticks.update(
                tickUpper,
                tick,
                liquidityDelta,
                _feeGrowthGlobal0X128,
                _feeGrowthGlobal1X128,
                secondsPerLiquidityCumulativeX128,
                tickCumulative,
                time,
                true,
                maxLiquidityPerTick
            );

            if (flippedLower) {
                tickBitmap.flipTick(tickLower, tickSpacing);
            }
            if (flippedUpper) {
                tickBitmap.flipTick(tickUpper, tickSpacing);
            }
        }

        (uint256 feeGrowthInside0X128, uint256 feeGrowthInside1X128) =
            ticks.getFeeGrowthInside(tickLower, tickUpper, tick, _feeGrowthGlobal0X128, _feeGrowthGlobal1X128);

        position.update(liquidityDelta, feeGrowthInside0X128, feeGrowthInside1X128);

        // clear any tick data that is no longer needed
        if (liquidityDelta < 0) {
            if (flippedLower) {
                ticks.clear(tickLower);
            }
            if (flippedUpper) {
                ticks.clear(tickUpper);
            }
        }
    }

    /// @inheritdoc IUniswapV3PoolActions
    /// @dev noDelegateCall is applied indirectly via _modifyPosition
    function mint(
        address recipient,
        int24 tickLower,
        int24 tickUpper,
        uint128 amount,
        bytes calldata data
    ) external override lock returns (uint256 amount0, uint256 amount1) {
        require(amount > 0);
        (, int256 amount0Int, int256 amount1Int) =
            _modifyPosition(
                ModifyPositionParams({
                    owner: recipient,
                    tickLower: tickLower,
                    tickUpper: tickUpper,
                    liquidityDelta: int256(amount).toInt128()
                })
            );

        amount0 = uint256(amount0Int);
        amount1 = uint256(amount1Int);

        uint256 balance0Before;
        uint256 balance1Before;
        if (amount0 > 0) balance0Before = balance0();
        if (amount1 > 0) balance1Before = balance1();
        IUniswapV3MintCallback(msg.sender).uniswapV3MintCallback(amount0, amount1, data);
        if (amount0 > 0) require(balance0Before.add(amount0) <= balance0(), 'M0');
        if (amount1 > 0) require(balance1Before.add(amount1) <= balance1(), 'M1');

        emit Mint(msg.sender, recipient, tickLower, tickUpper, amount, amount0, amount1);
    }

    /// @inheritdoc IUniswapV3PoolActions
    function collect(
        address recipient,
        int24 tickLower,
        int24 tickUpper,
        uint128 amount0Requested,
        uint128 amount1Requested
    ) external override lock returns (uint128 amount0, uint128 amount1) {
        // we don't need to checkTicks here, because invalid positions will never have non-zero tokensOwed{0,1}
        Position.Info storage position = positions.get(msg.sender, tickLower, tickUpper);

        amount0 = amount0Requested > position.tokensOwed0 ? position.tokensOwed0 : amount0Requested;
        amount1 = amount1Requested > position.tokensOwed1 ? position.tokensOwed1 : amount1Requested;

        if (amount0 > 0) {
            position.tokensOwed0 -= amount0;
            TransferHelper.safeTransfer(token0, recipient, amount0);
        }
        if (amount1 > 0) {
            position.tokensOwed1 -= amount1;
            TransferHelper.safeTransfer(token1, recipient, amount1);
        }

        emit Collect(msg.sender, recipient, tickLower, tickUpper, amount0, amount1);
    }

    /// @inheritdoc IUniswapV3PoolActions
    /// @dev noDelegateCall is applied indirectly via _modifyPosition
    function burn(
        int24 tickLower,
        int24 tickUpper,
        uint128 amount
    ) external override lock returns (uint256 amount0, uint256 amount1) {
        (Position.Info storage position, int256 amount0Int, int256 amount1Int) =
            _modifyPosition(
                ModifyPositionParams({
                    owner: msg.sender,
                    tickLower: tickLower,
                    tickUpper: tickUpper,
                    liquidityDelta: -int256(amount).toInt128()
                })
            );

        amount0 = uint256(-amount0Int);
        amount1 = uint256(-amount1Int);

        if (amount0 > 0 || amount1 > 0) {
            (position.tokensOwed0, position.tokensOwed1) = (
                position.tokensOwed0 + uint128(amount0),
                position.tokensOwed1 + uint128(amount1)
            );
        }

        emit Burn(msg.sender, tickLower, tickUpper, amount, amount0, amount1);
    }

    struct SwapCache {
        // the protocol fee for the input token
        uint8 feeProtocol;
        // liquidity at the beginning of the swap
        uint128 liquidityStart;
        // the timestamp of the current block
        uint32 blockTimestamp;
        // the current value of the tick accumulator, computed only if we cross an initialized tick
        int56 tickCumulative;
        // the current value of seconds per liquidity accumulator, computed only if we cross an initialized tick
        uint160 secondsPerLiquidityCumulativeX128;
        // whether we've computed and cached the above two accumulators
        bool computedLatestObservation;
    }

    // the top level state of the swap, the results of which are recorded in storage at the end
    struct SwapState {
        // the amount remaining to be swapped in/out of the input/output asset
        int256 amountSpecifiedRemaining;
        // the amount already swapped out/in of the output/input asset
        int256 amountCalculated;
        // current sqrt(price)
        uint160 sqrtPriceX96;
        // the tick associated with the current price
        int24 tick;
        // the global fee growth of the input token
        uint256 feeGrowthGlobalX128;
        // amount of input token paid as protocol fee
        uint128 protocolFee;
        // the current liquidity in range
        uint128 liquidity;
    }

    struct StepComputations {
        // the price at the beginning of the step
        uint160 sqrtPriceStartX96;
        // the next tick to swap to from the current tick in the swap direction
        int24 tickNext;
        // whether tickNext is initialized or not
        bool initialized;
        // sqrt(price) for the next tick (1/0)
        uint160 sqrtPriceNextX96;
        // how much is being swapped in in this step
        uint256 amountIn;
        // how much is being swapped out
        uint256 amountOut;
        // how much fee is being paid in
        uint256 feeAmount;
    }

    /// @inheritdoc IUniswapV3PoolActions
    function swap(
        address recipient,
        bool zeroForOne,
        int256 amountSpecified,
        uint160 sqrtPriceLimitX96,
        bytes calldata data
    ) external override noDelegateCall returns (int256 amount0, int256 amount1) {
        require(amountSpecified != 0, 'AS');

        Slot0 memory slot0Start = slot0;

        require(slot0Start.unlocked, 'LOK');
        require(
            zeroForOne
                ? sqrtPriceLimitX96 < slot0Start.sqrtPriceX96 && sqrtPriceLimitX96 > TickMath.MIN_SQRT_RATIO
                : sqrtPriceLimitX96 > slot0Start.sqrtPriceX96 && sqrtPriceLimitX96 < TickMath.MAX_SQRT_RATIO,
            'SPL'
        );

        slot0.unlocked = false;

        SwapCache memory cache =
            SwapCache({
                liquidityStart: liquidity,
                blockTimestamp: _blockTimestamp(),
                feeProtocol: zeroForOne ? (slot0Start.feeProtocol % 16) : (slot0Start.feeProtocol >> 4),
                secondsPerLiquidityCumulativeX128: 0,
                tickCumulative: 0,
                computedLatestObservation: false
            });

        bool exactInput = amountSpecified > 0;

        SwapState memory state =
            SwapState({
                amountSpecifiedRemaining: amountSpecified,
                amountCalculated: 0,
                sqrtPriceX96: slot0Start.sqrtPriceX96,
                tick: slot0Start.tick,
                feeGrowthGlobalX128: zeroForOne ? feeGrowthGlobal0X128 : feeGrowthGlobal1X128,
                protocolFee: 0,
                liquidity: cache.liquidityStart
            });

        // continue swapping as long as we haven't used the entire input/output and haven't reached the price limit
        while (state.amountSpecifiedRemaining != 0 && state.sqrtPriceX96 != sqrtPriceLimitX96) {
            StepComputations memory step;

            step.sqrtPriceStartX96 = state.sqrtPriceX96;

            (step.tickNext, step.initialized) = tickBitmap.nextInitializedTickWithinOneWord(
                state.tick,
                tickSpacing,
                zeroForOne
            );

            // ensure that we do not overshoot the min/max tick, as the tick bitmap is not aware of these bounds
            if (step.tickNext < TickMath.MIN_TICK) {
                step.tickNext = TickMath.MIN_TICK;
            } else if (step.tickNext > TickMath.MAX_TICK) {
                step.tickNext = TickMath.MAX_TICK;
            }

            // get the price for the next tick
            step.sqrtPriceNextX96 = TickMath.getSqrtRatioAtTick(step.tickNext);

            // compute values to swap to the target tick, price limit, or point where input/output amount is exhausted
            (state.sqrtPriceX96, step.amountIn, step.amountOut, step.feeAmount) = SwapMath.computeSwapStep(
                state.sqrtPriceX96,
                (zeroForOne ? step.sqrtPriceNextX96 < sqrtPriceLimitX96 : step.sqrtPriceNextX96 > sqrtPriceLimitX96)
                    ? sqrtPriceLimitX96
                    : step.sqrtPriceNextX96,
                state.liquidity,
                state.amountSpecifiedRemaining,
                fee
            );

            if (exactInput) {
                state.amountSpecifiedRemaining -= (step.amountIn + step.feeAmount).toInt256();
                state.amountCalculated = state.amountCalculated.sub(step.amountOut.toInt256());
            } else {
                state.amountSpecifiedRemaining += step.amountOut.toInt256();
                state.amountCalculated = state.amountCalculated.add((step.amountIn + step.feeAmount).toInt256());
            }

            // if the protocol fee is on, calculate how much is owed, decrement feeAmount, and increment protocolFee
            if (cache.feeProtocol > 0) {
                uint256 delta = step.feeAmount / cache.feeProtocol;
                step.feeAmount -= delta;
                state.protocolFee += uint128(delta);
            }

            // update global fee tracker
            if (state.liquidity > 0)
                state.feeGrowthGlobalX128 += FullMath.mulDiv(step.feeAmount, FixedPoint128.Q128, state.liquidity);

            // shift tick if we reached the next price
            if (state.sqrtPriceX96 == step.sqrtPriceNextX96) {
                // if the tick is initialized, run the tick transition
                if (step.initialized) {
                    // check for the placeholder value, which we replace with the actual value the first time the swap
                    // crosses an initialized tick
                    if (!cache.computedLatestObservation) {
                        (cache.tickCumulative, cache.secondsPerLiquidityCumulativeX128) = observations.observeSingle(
                            cache.blockTimestamp,
                            0,
                            slot0Start.tick,
                            slot0Start.observationIndex,
                            cache.liquidityStart,
                            slot0Start.observationCardinality
                        );
                        cache.computedLatestObservation = true;
                    }
                    int128 liquidityNet =
                        ticks.cross(
                            step.tickNext,
                            (zeroForOne ? state.feeGrowthGlobalX128 : feeGrowthGlobal0X128),
                            (zeroForOne ? feeGrowthGlobal1X128 : state.feeGrowthGlobalX128),
                            cache.secondsPerLiquidityCumulativeX128,
                            cache.tickCumulative,
                            cache.blockTimestamp
                        );
                    // if we're moving leftward, we interpret liquidityNet as the opposite sign
                    // safe because liquidityNet cannot be type(int128).min
                    if (zeroForOne) liquidityNet = -liquidityNet;

                    state.liquidity = LiquidityMath.addDelta(state.liquidity, liquidityNet);
                }

                state.tick = zeroForOne ? step.tickNext - 1 : step.tickNext;
            } else if (state.sqrtPriceX96 != step.sqrtPriceStartX96) {
                // recompute unless we're on a lower tick boundary (i.e. already transitioned ticks), and haven't moved
                state.tick = TickMath.getTickAtSqrtRatio(state.sqrtPriceX96);
            }
        }

        // update tick and write an oracle entry if the tick change
        if (state.tick != slot0Start.tick) {
            (uint16 observationIndex, uint16 observationCardinality) =
                observations.write(
                    slot0Start.observationIndex,
                    cache.blockTimestamp,
                    slot0Start.tick,
                    cache.liquidityStart,
                    slot0Start.observationCardinality,
                    slot0Start.observationCardinalityNext
                );
            (slot0.sqrtPriceX96, slot0.tick, slot0.observationIndex, slot0.observationCardinality) = (
                state.sqrtPriceX96,
                state.tick,
                observationIndex,
                observationCardinality
            );
        } else {
            // otherwise just update the price
            slot0.sqrtPriceX96 = state.sqrtPriceX96;
        }

        // update liquidity if it changed
        if (cache.liquidityStart != state.liquidity) liquidity = state.liquidity;

        // update fee growth global and, if necessary, protocol fees
        // overflow is acceptable, protocol has to withdraw before it hits type(uint128).max fees
        if (zeroForOne) {
            feeGrowthGlobal0X128 = state.feeGrowthGlobalX128;
            if (state.protocolFee > 0) protocolFees.token0 += state.protocolFee;
        } else {
            feeGrowthGlobal1X128 = state.feeGrowthGlobalX128;
            if (state.protocolFee > 0) protocolFees.token1 += state.protocolFee;
        }

        (amount0, amount1) = zeroForOne == exactInput
            ? (amountSpecified - state.amountSpecifiedRemaining, state.amountCalculated)
            : (state.amountCalculated, amountSpecified - state.amountSpecifiedRemaining);

        // do the transfers and collect payment
        if (zeroForOne) {
            if (amount1 < 0) TransferHelper.safeTransfer(token1, recipient, uint256(-amount1));

            uint256 balance0Before = balance0();
            IUniswapV3SwapCallback(msg.sender).uniswapV3SwapCallback(amount0, amount1, data);
            require(balance0Before.add(uint256(amount0)) <= balance0(), 'IIA');
        } else {
            if (amount0 < 0) TransferHelper.safeTransfer(token0, recipient, uint256(-amount0));

            uint256 balance1Before = balance1();
            IUniswapV3SwapCallback(msg.sender).uniswapV3SwapCallback(amount0, amount1, data);
            require(balance1Before.add(uint256(amount1)) <= balance1(), 'IIA');
        }

        emit Swap(msg.sender, recipient, amount0, amount1, state.sqrtPriceX96, state.liquidity, state.tick);
        slot0.unlocked = true;
    }

    /// @inheritdoc IUniswapV3PoolActions
    function flash(
        address recipient,
        uint256 amount0,
        uint256 amount1,
        bytes calldata data
    ) external override lock noDelegateCall {
        uint128 _liquidity = liquidity;
        require(_liquidity > 0, 'L');

        uint256 fee0 = FullMath.mulDivRoundingUp(amount0, fee, 1e6);
        uint256 fee1 = FullMath.mulDivRoundingUp(amount1, fee, 1e6);
        uint256 balance0Before = balance0();
        uint256 balance1Before = balance1();

        if (amount0 > 0) TransferHelper.safeTransfer(token0, recipient, amount0);
        if (amount1 > 0) TransferHelper.safeTransfer(token1, recipient, amount1);

        IUniswapV3FlashCallback(msg.sender).uniswapV3FlashCallback(fee0, fee1, data);

        uint256 balance0After = balance0();
        uint256 balance1After = balance1();

        require(balance0Before.add(fee0) <= balance0After, 'F0');
        require(balance1Before.add(fee1) <= balance1After, 'F1');

        // sub is safe because we know balanceAfter is gt balanceBefore by at least fee
        uint256 paid0 = balance0After - balance0Before;
        uint256 paid1 = balance1After - balance1Before;

        if (paid0 > 0) {
            uint8 feeProtocol0 = slot0.feeProtocol % 16;
            uint256 fees0 = feeProtocol0 == 0 ? 0 : paid0 / feeProtocol0;
            if (uint128(fees0) > 0) protocolFees.token0 += uint128(fees0);
            feeGrowthGlobal0X128 += FullMath.mulDiv(paid0 - fees0, FixedPoint128.Q128, _liquidity);
        }
        if (paid1 > 0) {
            uint8 feeProtocol1 = slot0.feeProtocol >> 4;
            uint256 fees1 = feeProtocol1 == 0 ? 0 : paid1 / feeProtocol1;
            if (uint128(fees1) > 0) protocolFees.token1 += uint128(fees1);
            feeGrowthGlobal1X128 += FullMath.mulDiv(paid1 - fees1, FixedPoint128.Q128, _liquidity);
        }

        emit Flash(msg.sender, recipient, amount0, amount1, paid0, paid1);
    }

    /// @inheritdoc IUniswapV3PoolOwnerActions
    function setFeeProtocol(uint8 feeProtocol0, uint8 feeProtocol1) external override lock onlyFactoryOwner {
        require(
            (feeProtocol0 == 0 || (feeProtocol0 >= 4 && feeProtocol0 <= 10)) &&
                (feeProtocol1 == 0 || (feeProtocol1 >= 4 && feeProtocol1 <= 10))
        );
        uint8 feeProtocolOld = slot0.feeProtocol;
        slot0.feeProtocol = feeProtocol0 + (feeProtocol1 << 4);
        emit SetFeeProtocol(feeProtocolOld % 16, feeProtocolOld >> 4, feeProtocol0, feeProtocol1);
    }

    /// @inheritdoc IUniswapV3PoolOwnerActions
    function collectProtocol(
        address recipient,
        uint128 amount0Requested,
        uint128 amount1Requested
    ) external override lock onlyFactoryOwner returns (uint128 amount0, uint128 amount1) {
        amount0 = amount0Requested > protocolFees.token0 ? protocolFees.token0 : amount0Requested;
        amount1 = amount1Requested > protocolFees.token1 ? protocolFees.token1 : amount1Requested;

        if (amount0 > 0) {
            if (amount0 == protocolFees.token0) amount0--; // ensure that the slot is not cleared, for gas savings
            protocolFees.token0 -= amount0;
            TransferHelper.safeTransfer(token0, recipient, amount0);
        }
        if (amount1 > 0) {
            if (amount1 == protocolFees.token1) amount1--; // ensure that the slot is not cleared, for gas savings
            protocolFees.token1 -= amount1;
            TransferHelper.safeTransfer(token1, recipient, amount1);
        }

        emit CollectProtocol(msg.sender, recipient, amount0, amount1);
    }
}

Changed text

Open file

contract UniswapV3Pool is IUniswapV3Pool, NoDelegateCall {
    using LowGasSafeMath for uint256;
    using LowGasSafeMath for int256;
    using SafeCast for uint256;
    using SafeCast for int256;
    using Tick for mapping(int24 => Tick.Info);
    using TickBitmap for mapping(int16 => uint256);
    using Position for mapping(bytes32 => Position.Info);
    using Position for Position.Info;
    using Oracle for Oracle.Observation[65535];

    /// @inheritdoc IUniswapV3PoolImmutables
    address public immutable override factory;
    /// @inheritdoc IUniswapV3PoolImmutables
    address public immutable override token0;
    /// @inheritdoc IUniswapV3PoolImmutables
    address public immutable override token1;
    /// @inheritdoc IUniswapV3PoolImmutables
    uint24 public immutable override fee;

    /// @inheritdoc IUniswapV3PoolImmutables
    int24 public immutable override tickSpacing;

    /// @inheritdoc IUniswapV3PoolImmutables
    uint128 public immutable override maxLiquidityPerTick;

    struct Slot0 {
        // the current price
        uint160 sqrtPriceX96;
        // the current tick
        int24 tick;
        // the most-recently updated index of the observations array
        uint16 observationIndex;
        // the current maximum number of observations that are being stored
        uint16 observationCardinality;
        // the next maximum number of observations to store, triggered in observations.write
        uint16 observationCardinalityNext;
        // the current protocol fee as a percentage of the swap fee taken on withdrawal
        // represented as an integer denominator (1/x)%
        uint8 feeProtocol;
        // whether the pool is locked
        bool unlocked;
    }
    /// @inheritdoc IUniswapV3PoolState
    Slot0 public override slot0;

    /// @inheritdoc IUniswapV3PoolState
    uint256 public override feeGrowthGlobal0X128;
    /// @inheritdoc IUniswapV3PoolState
    uint256 public override feeGrowthGlobal1X128;

    // accumulated protocol fees in token0/token1 units
    struct ProtocolFees {
        uint128 token0;
        uint128 token1;
    }
    /// @inheritdoc IUniswapV3PoolState
    ProtocolFees public override protocolFees;

    /// @inheritdoc IUniswapV3PoolState
    uint128 public override liquidity;

    /// @inheritdoc IUniswapV3PoolState
    mapping(int24 => Tick.Info) public override ticks;
    /// @inheritdoc IUniswapV3PoolState
    mapping(int16 => uint256) public override tickBitmap;
    /// @inheritdoc IUniswapV3PoolState
    mapping(bytes32 => Position.Info) public override positions;
    /// @inheritdoc IUniswapV3PoolState
    Oracle.Observation[65535] public override observations;

    /// @dev Mutually exclusive reentrancy protection into the pool to/from a method. This method also prevents entrance
    /// to a function before the pool is initialized. The reentrancy guard is required throughout the contract because
    /// we use balance checks to determine the payment status of interactions such as mint, swap and flash.
    modifier lock() {
        require(slot0.unlocked, 'LOK');
        slot0.unlocked = false;
        _;
        slot0.unlocked = true;
    }

    /// @dev Prevents calling a function from anyone except the address returned by IUniswapV3Factory#owner()
    modifier onlyFactoryOwner() {
        require(msg.sender == IUniswapV3Factory(factory).owner());
        _;
    }

    constructor() {
        int24 _tickSpacing;
        (factory, token0, token1, fee, _tickSpacing) = IUniswapV3PoolDeployer(msg.sender).parameters();
        tickSpacing = _tickSpacing;

        maxLiquidityPerTick = Tick.tickSpacingToMaxLiquidityPerTick(_tickSpacing);
    }

    /// @dev Common checks for valid tick inputs.
    function checkTicks(int24 tickLower, int24 tickUpper) private pure {
        require(tickLower < tickUpper, 'TLU');
        require(tickLower >= TickMath.MIN_TICK, 'TLM');
        require(tickUpper <= TickMath.MAX_TICK, 'TUM');
    }

    /// @dev Returns the block timestamp truncated to 32 bits, i.e. mod 2**32. This method is overridden in tests.
    function _blockTimestamp() internal view virtual returns (uint32) {
        return uint32(block.timestamp); // truncation is desired
    }

    /// @dev Get the pool's balance of token0
    /// @dev This function is gas optimized to avoid a redundant extcodesize check in addition to the returndatasize
    /// check
    function balance0() private view returns (uint256) {
        (bool success, bytes memory data) =
            token0.staticcall(abi.encodeWithSelector(IERC20Minimal.balanceOf.selector, address(this)));
        require(success && data.length >= 32);
        return abi.decode(data, (uint256));
    }

    /// @dev Get the pool's balance of token1
    /// @dev This function is gas optimized to avoid a redundant extcodesize check in addition to the returndatasize
    /// check
    function balance1() private view returns (uint256) {
        (bool success, bytes memory data) =
            token1.staticcall(abi.encodeWithSelector(IERC20Minimal.balanceOf.selector, address(this)));
        require(success && data.length >= 32);
        return abi.decode(data, (uint256));
    }

    /// @inheritdoc IUniswapV3PoolDerivedState
    function snapshotCumulativesInside(int24 tickLower, int24 tickUpper)
        external
        view
        override
        noDelegateCall
        returns (
            int56 tickCumulativeInside,
            uint160 secondsPerLiquidityInsideX128,
            uint32 secondsInside
        )
    {
        checkTicks(tickLower, tickUpper);

        int56 tickCumulativeLower;
        int56 tickCumulativeUpper;
        uint160 secondsPerLiquidityOutsideLowerX128;
        uint160 secondsPerLiquidityOutsideUpperX128;
        uint32 secondsOutsideLower;
        uint32 secondsOutsideUpper;

        {
            Tick.Info storage lower = ticks[tickLower];
            Tick.Info storage upper = ticks[tickUpper];
            bool initializedLower;
            (tickCumulativeLower, secondsPerLiquidityOutsideLowerX128, secondsOutsideLower, initializedLower) = (
                lower.tickCumulativeOutside,
                lower.secondsPerLiquidityOutsideX128,
                lower.secondsOutside,
                lower.initialized
            );
            require(initializedLower);

            bool initializedUpper;
            (tickCumulativeUpper, secondsPerLiquidityOutsideUpperX128, secondsOutsideUpper, initializedUpper) = (
                upper.tickCumulativeOutside,
                upper.secondsPerLiquidityOutsideX128,
                upper.secondsOutside,
                upper.initialized
            );
            require(initializedUpper);
        }

        Slot0 memory _slot0 = slot0;

        if (_slot0.tick < tickLower) {
            return (
                tickCumulativeLower - tickCumulativeUpper,
                secondsPerLiquidityOutsideLowerX128 - secondsPerLiquidityOutsideUpperX128,
                secondsOutsideLower - secondsOutsideUpper
            );
        } else if (_slot0.tick < tickUpper) {
            uint32 time = _blockTimestamp();
            (int56 tickCumulative, uint160 secondsPerLiquidityCumulativeX128) =
                observations.observeSingle(
                    time,
                    0,
                    _slot0.tick,
                    _slot0.observationIndex,
                    liquidity,
                    _slot0.observationCardinality
                );
            return (
                tickCumulative - tickCumulativeLower - tickCumulativeUpper,
                secondsPerLiquidityCumulativeX128 -
                    secondsPerLiquidityOutsideLowerX128 -
                    secondsPerLiquidityOutsideUpperX128,
                time - secondsOutsideLower - secondsOutsideUpper
            );
        } else {
            return (
                tickCumulativeUpper - tickCumulativeLower,
                secondsPerLiquidityOutsideUpperX128 - secondsPerLiquidityOutsideLowerX128,
                secondsOutsideUpper - secondsOutsideLower
            );
        }
    }

    /// @inheritdoc IUniswapV3PoolDerivedState
    function observe(uint32[] calldata secondsAgos)
        external
        view
        override
        noDelegateCall
        returns (int56[] memory tickCumulatives, uint160[] memory secondsPerLiquidityCumulativeX128s)
    {
        return
            observations.observe(
                _blockTimestamp(),
                secondsAgos,
                slot0.tick,
                slot0.observationIndex,
                liquidity,
                slot0.observationCardinality
            );
    }

    /// @inheritdoc IUniswapV3PoolActions
    function increaseObservationCardinalityNext(uint16 observationCardinalityNext)
        external
        override
        lock
        noDelegateCall
    {
        uint16 observationCardinalityNextOld = slot0.observationCardinalityNext; // for the event
        uint16 observationCardinalityNextNew =
            observations.grow(observationCardinalityNextOld, observationCardinalityNext);
        slot0.observationCardinalityNext = observationCardinalityNextNew;
        if (observationCardinalityNextOld != observationCardinalityNextNew)
            emit IncreaseObservationCardinalityNext(observationCardinalityNextOld, observationCardinalityNextNew);
    }

    /// @inheritdoc IUniswapV3PoolActions
    /// @dev not locked because it initializes unlocked
    function initialize(uint160 sqrtPriceX96) external override {
        require(slot0.sqrtPriceX96 == 0, 'AI');

        int24 tick = TickMath.getTickAtSqrtRatio(sqrtPriceX96);

        (uint16 cardinality, uint16 cardinalityNext) = observations.initialize(_blockTimestamp());

        slot0 = Slot0({
            sqrtPriceX96: sqrtPriceX96,
            tick: tick,
            observationIndex: 0,
            observationCardinality: cardinality,
            observationCardinalityNext: cardinalityNext,
            feeProtocol: 0,
            unlocked: true
        });

        emit Initialize(sqrtPriceX96, tick);
    }

    struct ModifyPositionParams {
        // the address that owns the position
        address owner;
        // the lower and upper tick of the position
        int24 tickLower;
        int24 tickUpper;
        // any change in liquidity
        int128 liquidityDelta;
    }

    /// @dev Effect some changes to a position
    /// @param params the position details and the change to the position's liquidity to effect
    /// @return position a storage pointer referencing the position with the given owner and tick range
    /// @return amount0 the amount of token0 owed to the pool, negative if the pool should pay the recipient
    /// @return amount1 the amount of token1 owed to the pool, negative if the pool should pay the recipient
    function _modifyPosition(ModifyPositionParams memory params)
        private
        noDelegateCall
        returns (
            Position.Info storage position,
            int256 amount0,
            int256 amount1
        )
    {
        checkTicks(params.tickLower, params.tickUpper);

        Slot0 memory _slot0 = slot0; // SLOAD for gas optimization

        position = _updatePosition(
            params.owner,
            params.tickLower,
            params.tickUpper,
            params.liquidityDelta,
            _slot0.tick
        );

        if (params.liquidityDelta != 0) {
            if (_slot0.tick < params.tickLower) {
                // current tick is below the passed range; liquidity can only become in range by crossing from left to
                // right, when we'll need _more_ token0 (it's becoming more valuable) so user must provide it
                amount0 = SqrtPriceMath.getAmount0Delta(
                    TickMath.getSqrtRatioAtTick(params.tickLower),
                    TickMath.getSqrtRatioAtTick(params.tickUpper),
                    params.liquidityDelta
                );
            } else if (_slot0.tick < params.tickUpper) {
                // current tick is inside the passed range
                uint128 liquidityBefore = liquidity; // SLOAD for gas optimization

                // write an oracle entry
                (slot0.observationIndex, slot0.observationCardinality) = observations.write(
                    _slot0.observationIndex,
                    _blockTimestamp(),
                    _slot0.tick,
                    liquidityBefore,
                    _slot0.observationCardinality,
                    _slot0.observationCardinalityNext
                );

                amount0 = SqrtPriceMath.getAmount0Delta(
                    _slot0.sqrtPriceX96,
                    TickMath.getSqrtRatioAtTick(params.tickUpper),
                    params.liquidityDelta
                );
                amount1 = SqrtPriceMath.getAmount1Delta(
                    TickMath.getSqrtRatioAtTick(params.tickLower),
                    _slot0.sqrtPriceX96,
                    params.liquidityDelta
                );

                liquidity = LiquidityMath.addDelta(liquidityBefore, params.liquidityDelta);
            } else {
                // current tick is above the passed range; liquidity can only become in range by crossing from right to
                // left, when we'll need _more_ token1 (it's becoming more valuable) so user must provide it
                amount1 = SqrtPriceMath.getAmount1Delta(
                    TickMath.getSqrtRatioAtTick(params.tickLower),
                    TickMath.getSqrtRatioAtTick(params.tickUpper),
                    params.liquidityDelta
                );
            }
        }
    }

    /// @dev Gets and updates a position with the given liquidity delta
    /// @param owner the owner of the position
    /// @param tickLower the lower tick of the position's tick range
    /// @param tickUpper the upper tick of the position's tick range
    /// @param tick the current tick, passed to avoid sloads
    function _updatePosition(
        address owner,
        int24 tickLower,
        int24 tickUpper,
        int128 liquidityDelta,
        int24 tick
    ) private returns (Position.Info storage position) {
        position = positions.get(owner, tickLower, tickUpper);

        uint256 _feeGrowthGlobal0X128 = feeGrowthGlobal0X128; // SLOAD for gas optimization
        uint256 _feeGrowthGlobal1X128 = feeGrowthGlobal1X128; // SLOAD for gas optimization

        // if we need to update the ticks, do it
        bool flippedLower;
        bool flippedUpper;
        if (liquidityDelta != 0) {
            uint32 time = _blockTimestamp();
            (int56 tickCumulative, uint160 secondsPerLiquidityCumulativeX128) =
                observations.observeSingle(
                    time,
                    0,
                    slot0.tick,
                    slot0.observationIndex,
                    liquidity,
                    slot0.observationCardinality
                );

            flippedLower = ticks.update(
                tickLower,
                tick,
                liquidityDelta,
                _feeGrowthGlobal0X128,
                _feeGrowthGlobal1X128,
                secondsPerLiquidityCumulativeX128,
                tickCumulative,
                time,
                false,
                maxLiquidityPerTick
            );
            flippedUpper = ticks.update(
                tickUpper,
                tick,
                liquidityDelta,
                _feeGrowthGlobal0X128,
                _feeGrowthGlobal1X128,
                secondsPerLiquidityCumulativeX128,
                tickCumulative,
                time,
                true,
                maxLiquidityPerTick
            );

            if (flippedLower) {
                tickBitmap.flipTick(tickLower, tickSpacing);
            }
            if (flippedUpper) {
                tickBitmap.flipTick(tickUpper, tickSpacing);
            }
        }

        (uint256 feeGrowthInside0X128, uint256 feeGrowthInside1X128) =
            ticks.getFeeGrowthInside(tickLower, tickUpper, tick, _feeGrowthGlobal0X128, _feeGrowthGlobal1X128);

        position.update(liquidityDelta, feeGrowthInside0X128, feeGrowthInside1X128);

        // clear any tick data that is no longer needed
        if (liquidityDelta < 0) {
            if (flippedLower) {
                ticks.clear(tickLower);
            }
            if (flippedUpper) {
                ticks.clear(tickUpper);
            }
        }
    }

    /// @inheritdoc IUniswapV3PoolActions
    /// @dev noDelegateCall is applied indirectly via _modifyPosition
    function mint(
        address recipient,
        int24 tickLower,
        int24 tickUpper,
        uint128 amount,
        bytes calldata data
    ) external override lock returns (uint256 amount0, uint256 amount1) {
        require(amount > 0);
        (, int256 amount0Int, int256 amount1Int) =
            _modifyPosition(
                ModifyPositionParams({
                    owner: recipient,
                    tickLower: tickLower,
                    tickUpper: tickUpper,
                    liquidityDelta: int256(amount).toInt128()
                })
            );

        amount0 = uint256(amount0Int);
        amount1 = uint256(amount1Int);

        uint256 balance0Before;
        uint256 balance1Before;
        if (amount0 > 0) balance0Before = balance0();
        if (amount1 > 0) balance1Before = balance1();
        IUniswapV3MintCallback(msg.sender).uniswapV3MintCallback(amount0, amount1, data);
        if (amount0 > 0) require(balance0Before.add(amount0) <= balance0(), 'M0');
        if (amount1 > 0) require(balance1Before.add(amount1) <= balance1(), 'M1');

        emit Mint(msg.sender, recipient, tickLower, tickUpper, amount, amount0, amount1);
    }

    /// @inheritdoc IUniswapV3PoolActions
    function collect(
        address recipient,
        int24 tickLower,
        int24 tickUpper,
        uint128 amount0Requested,
        uint128 amount1Requested
    ) external override lock returns (uint128 amount0, uint128 amount1) {
        // we don't need to checkTicks here, because invalid positions will never have non-zero tokensOwed{0,1}
        Position.Info storage position = positions.get(msg.sender, tickLower, tickUpper);

        amount0 = amount0Requested > position.tokensOwed0 ? position.tokensOwed0 : amount0Requested;
        amount1 = amount1Requested > position.tokensOwed1 ? position.tokensOwed1 : amount1Requested;

        if (amount0 > 0) {
            position.tokensOwed0 -= amount0;
            TransferHelper.safeTransfer(token0, recipient, amount0);
        }
        if (amount1 > 0) {
            position.tokensOwed1 -= amount1;
            TransferHelper.safeTransfer(token1, recipient, amount1);
        }

        emit Collect(msg.sender, recipient, tickLower, tickUpper, amount0, amount1);
    }

    /// @inheritdoc IUniswapV3PoolActions
    /// @dev noDelegateCall is applied indirectly via _modifyPosition
    function burn(
        int24 tickLower,
        int24 tickUpper,
        uint128 amount
    ) external override lock returns (uint256 amount0, uint256 amount1) {
        (Position.Info storage position, int256 amount0Int, int256 amount1Int) =
            _modifyPosition(
                ModifyPositionParams({
                    owner: msg.sender,
                    tickLower: tickLower,
                    tickUpper: tickUpper,
                    liquidityDelta: -int256(amount).toInt128()
                })
            );

        amount0 = uint256(-amount0Int);
        amount1 = uint256(-amount1Int);

        if (amount0 > 0 || amount1 > 0) {
            (position.tokensOwed0, position.tokensOwed1) = (
                position.tokensOwed0 + uint128(amount0),
                position.tokensOwed1 + uint128(amount1)
            );
        }

        emit Burn(msg.sender, tickLower, tickUpper, amount, amount0, amount1);
    }

    struct SwapCache {
        // the protocol fee for the input token
        uint8 feeProtocol;
        // liquidity at the beginning of the swap
        uint128 liquidityStart;
        // the timestamp of the current block
        uint32 blockTimestamp;
        // the current value of the tick accumulator, computed only if we cross an initialized tick
        int56 tickCumulative;
        // the current value of seconds per liquidity accumulator, computed only if we cross an initialized tick
        uint160 secondsPerLiquidityCumulativeX128;
        // whether we've computed and cached the above two accumulators
        bool computedLatestObservation;
    }

    // the top level state of the swap, the results of which are recorded in storage at the end
    struct SwapState {
        // the amount remaining to be swapped in/out of the input/output asset
        int256 amountSpecifiedRemaining;
        // the amount already swapped out/in of the output/input asset
        int256 amountCalculated;
        // current sqrt(price)
        uint160 sqrtPriceX96;
        // the tick associated with the current price
        int24 tick;
        // the global fee growth of the input token
        uint256 feeGrowthGlobalX128;
        // amount of input token paid as protocol fee
        uint128 protocolFee;
        // the current liquidity in range
        uint128 liquidity;
    }

    struct StepComputations {
        // the price at the beginning of the step
        uint160 sqrtPriceStartX96;
        // the next tick to swap to from the current tick in the swap direction
        int24 tickNext;
        // whether tickNext is initialized or not
        bool initialized;
        // sqrt(price) for the next tick (1/0)
        uint160 sqrtPriceNextX96;
        // how much is being swapped in in this step
        uint256 amountIn;
        // how much is being swapped out
        uint256 amountOut;
        // how much fee is being paid in
        uint256 feeAmount;
    }

    /// @inheritdoc IUniswapV3PoolActions
    function swap(
        address recipient,
        bool zeroForOne,
        int256 amountSpecified,
        uint160 sqrtPriceLimitX96,
        bytes calldata data
    ) external override noDelegateCall returns (int256 amount0, int256 amount1) {
        require(amountSpecified != 0, 'AS');

        Slot0 memory slot0Start = slot0;

        require(slot0Start.unlocked, 'LOK');
        require(
            zeroForOne
                ? sqrtPriceLimitX96 < slot0Start.sqrtPriceX96 && sqrtPriceLimitX96 > TickMath.MIN_SQRT_RATIO
                : sqrtPriceLimitX96 > slot0Start.sqrtPriceX96 && sqrtPriceLimitX96 < TickMath.MAX_SQRT_RATIO,
            'SPL'
        );

        slot0.unlocked = false;

        SwapCache memory cache =
            SwapCache({
                liquidityStart: liquidity,
                blockTimestamp: _blockTimestamp(),
                feeProtocol: zeroForOne ? (slot0Start.feeProtocol % 16) : (slot0Start.feeProtocol >> 4),
                secondsPerLiquidityCumulativeX128: 0,
                tickCumulative: 0,
                computedLatestObservation: false
            });

        bool exactInput = amountSpecified > 0;

        SwapState memory state =
            SwapState({
                amountSpecifiedRemaining: amountSpecified,
                amountCalculated: 0,
                sqrtPriceX96: slot0Start.sqrtPriceX96,
                tick: slot0Start.tick,
                feeGrowthGlobalX128: zeroForOne ? feeGrowthGlobal0X128 : feeGrowthGlobal1X128,
                protocolFee: 0,
                liquidity: cache.liquidityStart
            });

        // continue swapping as long as we haven't used the entire input/output and haven't reached the price limit
        while (state.amountSpecifiedRemaining != 0 && state.sqrtPriceX96 != sqrtPriceLimitX96) {
            StepComputations memory step;

            step.sqrtPriceStartX96 = state.sqrtPriceX96;

            (step.tickNext, step.initialized) = tickBitmap.nextInitializedTickWithinOneWord(
                state.tick,
                tickSpacing,
                zeroForOne
            );

            // ensure that we do not overshoot the min/max tick, as the tick bitmap is not aware of these bounds
            if (step.tickNext < TickMath.MIN_TICK) {
                step.tickNext = TickMath.MIN_TICK;
            } else if (step.tickNext > TickMath.MAX_TICK) {
                step.tickNext = TickMath.MAX_TICK;
            }

            // get the price for the next tick
            step.sqrtPriceNextX96 = TickMath.getSqrtRatioAtTick(step.tickNext);

            // compute values to swap to the target tick, price limit, or point where input/output amount is exhausted
            (state.sqrtPriceX96, step.amountIn, step.amountOut, step.feeAmount) = SwapMath.computeSwapStep(
                state.sqrtPriceX96,
                (zeroForOne ? step.sqrtPriceNextX96 < sqrtPriceLimitX96 : step.sqrtPriceNextX96 > sqrtPriceLimitX96)
                    ? sqrtPriceLimitX96
                    : step.sqrtPriceNextX96,
                state.liquidity,
                state.amountSpecifiedRemaining,
                fee
            );

            if (exactInput) {
                state.amountSpecifiedRemaining -= (step.amountIn + step.feeAmount).toInt256();
                state.amountCalculated = state.amountCalculated.sub(step.amountOut.toInt256());
            } else {
                state.amountSpecifiedRemaining += step.amountOut.toInt256();
                state.amountCalculated = state.amountCalculated.add((step.amountIn + step.feeAmount).toInt256());
            }

            // if the protocol fee is on, calculate how much is owed, decrement feeAmount, and increment protocolFee
            if (cache.feeProtocol > 0) {
                uint256 delta = (step.feeAmount * cache.feeProtocol) / 15;
                step.feeAmount -= delta;
                state.protocolFee += uint128(delta);
            }

            // update global fee tracker
            if (state.liquidity > 0)
                state.feeGrowthGlobalX128 += FullMath.mulDiv(step.feeAmount, FixedPoint128.Q128, state.liquidity);

            // shift tick if we reached the next price
            if (state.sqrtPriceX96 == step.sqrtPriceNextX96) {
                // if the tick is initialized, run the tick transition
                if (step.initialized) {
                    // check for the placeholder value, which we replace with the actual value the first time the swap
                    // crosses an initialized tick
                    if (!cache.computedLatestObservation) {
                        (cache.tickCumulative, cache.secondsPerLiquidityCumulativeX128) = observations.observeSingle(
                            cache.blockTimestamp,
                            0,
                            slot0Start.tick,
                            slot0Start.observationIndex,
                            cache.liquidityStart,
                            slot0Start.observationCardinality
                        );
                        cache.computedLatestObservation = true;
                    }
                    int128 liquidityNet =
                        ticks.cross(
                            step.tickNext,
                            (zeroForOne ? state.feeGrowthGlobalX128 : feeGrowthGlobal0X128),
                            (zeroForOne ? feeGrowthGlobal1X128 : state.feeGrowthGlobalX128),
                            cache.secondsPerLiquidityCumulativeX128,
                            cache.tickCumulative,
                            cache.blockTimestamp
                        );
                    // if we're moving leftward, we interpret liquidityNet as the opposite sign
                    // safe because liquidityNet cannot be type(int128).min
                    if (zeroForOne) liquidityNet = -liquidityNet;

                    state.liquidity = LiquidityMath.addDelta(state.liquidity, liquidityNet);
                }

                state.tick = zeroForOne ? step.tickNext - 1 : step.tickNext;
            } else if (state.sqrtPriceX96 != step.sqrtPriceStartX96) {
                // recompute unless we're on a lower tick boundary (i.e. already transitioned ticks), and haven't moved
                state.tick = TickMath.getTickAtSqrtRatio(state.sqrtPriceX96);
            }
        }

        // update tick and write an oracle entry if the tick change
        if (state.tick != slot0Start.tick) {
            (uint16 observationIndex, uint16 observationCardinality) =
                observations.write(
                    slot0Start.observationIndex,
                    cache.blockTimestamp,
                    slot0Start.tick,
                    cache.liquidityStart,
                    slot0Start.observationCardinality,
                    slot0Start.observationCardinalityNext
                );
            (slot0.sqrtPriceX96, slot0.tick, slot0.observationIndex, slot0.observationCardinality) = (
                state.sqrtPriceX96,
                state.tick,
                observationIndex,
                observationCardinality
            );
        } else {
            // otherwise just update the price
            slot0.sqrtPriceX96 = state.sqrtPriceX96;
        }

        // update liquidity if it changed
        if (cache.liquidityStart != state.liquidity) liquidity = state.liquidity;

        // update fee growth global and, if necessary, protocol fees
        // overflow is acceptable, protocol has to withdraw before it hits type(uint128).max fees
        if (zeroForOne) {
            feeGrowthGlobal0X128 = state.feeGrowthGlobalX128;
            if (state.protocolFee > 0) protocolFees.token0 += state.protocolFee;
        } else {
            feeGrowthGlobal1X128 = state.feeGrowthGlobalX128;
            if (state.protocolFee > 0) protocolFees.token1 += state.protocolFee;
        }

        (amount0, amount1) = zeroForOne == exactInput
            ? (amountSpecified - state.amountSpecifiedRemaining, state.amountCalculated)
            : (state.amountCalculated, amountSpecified - state.amountSpecifiedRemaining);

        // do the transfers and collect payment
        if (zeroForOne) {
            if (amount1 < 0) TransferHelper.safeTransfer(token1, recipient, uint256(-amount1));

            uint256 balance0Before = balance0();
            IUniswapV3SwapCallback(msg.sender).uniswapV3SwapCallback(amount0, amount1, data);
            require(balance0Before.add(uint256(amount0)) <= balance0(), 'IIA');
        } else {
            if (amount0 < 0) TransferHelper.safeTransfer(token0, recipient, uint256(-amount0));

            uint256 balance1Before = balance1();
            IUniswapV3SwapCallback(msg.sender).uniswapV3SwapCallback(amount0, amount1, data);
            require(balance1Before.add(uint256(amount1)) <= balance1(), 'IIA');
        }

        emit Swap(msg.sender, recipient, amount0, amount1, state.sqrtPriceX96, state.liquidity, state.tick);
        slot0.unlocked = true;
    }

    /// @inheritdoc IUniswapV3PoolActions
    function flash(
        address recipient,
        uint256 amount0,
        uint256 amount1,
        bytes calldata data
    ) external override lock noDelegateCall {
        uint128 _liquidity = liquidity;
        require(_liquidity > 0, 'L');

        uint256 fee0 = FullMath.mulDivRoundingUp(amount0, fee, 1e6);
        uint256 fee1 = FullMath.mulDivRoundingUp(amount1, fee, 1e6);
        uint256 balance0Before = balance0();
        uint256 balance1Before = balance1();

        if (amount0 > 0) TransferHelper.safeTransfer(token0, recipient, amount0);
        if (amount1 > 0) TransferHelper.safeTransfer(token1, recipient, amount1);

        IUniswapV3FlashCallback(msg.sender).uniswapV3FlashCallback(fee0, fee1, data);

        uint256 balance0After = balance0();
        uint256 balance1After = balance1();

        require(balance0Before.add(fee0) <= balance0After, 'F0');
        require(balance1Before.add(fee1) <= balance1After, 'F1');

        // sub is safe because we know balanceAfter is gt balanceBefore by at least fee
        uint256 paid0 = balance0After - balance0Before;
        uint256 paid1 = balance1After - balance1Before;

        if (paid0 > 0) {
            uint8 feeProtocol0 = slot0.feeProtocol % 16;
            uint256 fees0 = (paid0 * feeProtocol0) / 15;
            if (uint128(fees0) > 0) protocolFees.token0 += uint128(fees0);
            feeGrowthGlobal0X128 += FullMath.mulDiv(paid0 - fees0, FixedPoint128.Q128, _liquidity);
        }
        if (paid1 > 0) {
            uint8 feeProtocol1 = slot0.feeProtocol >> 4;
            uint256 fees1 = (paid1 * feeProtocol1) / 15;
            if (uint128(fees1) > 0) protocolFees.token1 += uint128(fees1);
            feeGrowthGlobal1X128 += FullMath.mulDiv(paid1 - fees1, FixedPoint128.Q128, _liquidity);
        }

        emit Flash(msg.sender, recipient, amount0, amount1, paid0, paid1);
    }

    /// @inheritdoc IUniswapV3PoolOwnerActions
    function setFeeProtocol(uint8 feeProtocol0, uint8 feeProtocol1) external override lock onlyFactoryOwner {
        uint8 feeProtocolOld = slot0.feeProtocol;
        slot0.feeProtocol = feeProtocol0 + (feeProtocol1 << 4);
        emit SetFeeProtocol(feeProtocolOld % 16, feeProtocolOld >> 4, feeProtocol0, feeProtocol1);
    }

    /// @inheritdoc IUniswapV3PoolOwnerActions
    function collectProtocol(
        address recipient,
        uint128 amount0Requested,
        uint128 amount1Requested
    ) external override lock onlyFactoryOwner returns (uint128 amount0, uint128 amount1) {
        amount0 = amount0Requested > protocolFees.token0 ? protocolFees.token0 : amount0Requested;
        amount1 = amount1Requested > protocolFees.token1 ? protocolFees.token1 : amount1Requested;

        if (amount0 > 0) {
            if (amount0 == protocolFees.token0) amount0--; // ensure that the slot is not cleared, for gas savings
            protocolFees.token0 -= amount0;
            TransferHelper.safeTransfer(token0, recipient, amount0);
        }
        if (amount1 > 0) {
            if (amount1 == protocolFees.token1) amount1--; // ensure that the slot is not cleared, for gas savings
            protocolFees.token1 -= amount1;
            TransferHelper.safeTransfer(token1, recipient, amount1);
        }

        emit CollectProtocol(msg.sender, recipient, amount0, amount1);
    }
}