// File: contracts/interfaces/callback/ISolidlyV3FlashCallback.sol



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

/// @title Callback for ISolidlyV3PoolActions#flash
/// @notice Any contract that calls ISolidlyV3PoolActions#flash must implement this interface
interface ISolidlyV3FlashCallback {
    /// @notice Called to `msg.sender` after transferring to the recipient from ISolidlyV3Pool#flash.
    /// @dev In the implementation you must repay the pool the tokens sent by flash plus the computed fee amounts.
    /// The caller of this method must be checked to be a SolidlyV3Pool deployed by the canonical SolidlyV3Factory.
    /// @param fee0 The fee amount in token0 due to the pool by the end of the flash
    /// @param fee1 The fee amount in token1 due to the pool by the end of the flash
    /// @param data Any data passed through by the caller via the ISolidlyV3PoolActions#flash call
    function solidlyV3FlashCallback(uint256 fee0, uint256 fee1, bytes calldata data) external;
}

// File: contracts/interfaces/callback/ISolidlyV3MintCallback.sol



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

/// @title Callback for ISolidlyV3PoolActions#mint
/// @notice Any contract that calls ISolidlyV3PoolActions#mint must implement this interface
interface ISolidlyV3MintCallback {
    /// @notice Called to `msg.sender` after minting liquidity to a position from ISolidlyV3Pool#mint.
    /// @dev In the implementation you must pay the pool tokens owed for the minted liquidity.
    /// The caller of this method must be checked to be a SolidlyV3Pool deployed by the canonical SolidlyV3Factory.
    /// @param amount0Owed The amount of token0 due to the pool for the minted liquidity
    /// @param amount1Owed The amount of token1 due to the pool for the minted liquidity
    /// @param data Any data passed through by the caller via the ISolidlyV3PoolActions#mint call
    function solidlyV3MintCallback(uint256 amount0Owed, uint256 amount1Owed, bytes calldata data) external;
}

// File: contracts/interfaces/callback/ISolidlyV3SwapCallback.sol



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

/// @title Callback for ISolidlyV3PoolActions#swap
/// @notice Any contract that calls ISolidlyV3PoolActions#swap must implement this interface
interface ISolidlyV3SwapCallback {
    /// @notice Called to `msg.sender` after executing a swap via ISolidlyV3Pool#swap.
    /// @dev In the implementation you must pay the pool tokens owed for the swap.
    /// The caller of this method must be checked to be a SolidlyV3Pool deployed by the canonical SolidlyV3Factory.
    /// amount0Delta and amount1Delta can both be 0 if no tokens were swapped.
    /// @param amount0Delta The amount of token0 that was sent (negative) or must be received (positive) by the pool by
    /// the end of the swap. If positive, the callback must send that amount of token0 to the pool.
    /// @param amount1Delta The amount of token1 that was sent (negative) or must be received (positive) by the pool by
    /// the end of the swap. If positive, the callback must send that amount of token1 to the pool.
    /// @param data Any data passed through by the caller via the ISolidlyV3PoolActions#swap call
    function solidlyV3SwapCallback(int256 amount0Delta, int256 amount1Delta, bytes calldata data) external;
}

// File: contracts/interfaces/IERC20Minimal.sol



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

/// @title Minimal ERC20 interface for Solidly
/// @notice Contains a subset of the full ERC20 interface that is used in Solidly V3
interface IERC20Minimal {
    /// @notice Returns the balance of a token
    /// @param account The account for which to look up the number of tokens it has, i.e. its balance
    /// @return The number of tokens held by the account
    function balanceOf(address account) external view returns (uint256);

    /// @notice Transfers the amount of token from the `msg.sender` to the recipient
    /// @param recipient The account that will receive the amount transferred
    /// @param amount The number of tokens to send from the sender to the recipient
    /// @return Returns true for a successful transfer, false for an unsuccessful transfer
    function transfer(address recipient, uint256 amount) external returns (bool);

    /// @notice Returns the current allowance given to a spender by an owner
    /// @param owner The account of the token owner
    /// @param spender The account of the token spender
    /// @return The current allowance granted by `owner` to `spender`
    function allowance(address owner, address spender) external view returns (uint256);

    /// @notice Sets the allowance of a spender from the `msg.sender` to the value `amount`
    /// @param spender The account which will be allowed to spend a given amount of the owners tokens
    /// @param amount The amount of tokens allowed to be used by `spender`
    /// @return Returns true for a successful approval, false for unsuccessful
    function approve(address spender, uint256 amount) external returns (bool);

    /// @notice Transfers `amount` tokens from `sender` to `recipient` up to the allowance given to the `msg.sender`
    /// @param sender The account from which the transfer will be initiated
    /// @param recipient The recipient of the transfer
    /// @param amount The amount of the transfer
    /// @return Returns true for a successful transfer, false for unsuccessful
    function transferFrom(
        address sender,
        address recipient,
        uint256 amount
    ) external returns (bool);

    /// @notice Event emitted when tokens are transferred from one address to another, either via `#transfer` or `#transferFrom`.
    /// @param from The account from which the tokens were sent, i.e. the balance decreased
    /// @param to The account to which the tokens were sent, i.e. the balance increased
    /// @param value The amount of tokens that were transferred
    event Transfer(address indexed from, address indexed to, uint256 value);

    /// @notice Event emitted when the approval amount for the spender of a given owner's tokens changes.
    /// @param owner The account that approved spending of its tokens
    /// @param spender The account for which the spending allowance was modified
    /// @param value The new allowance from the owner to the spender
    event Approval(address indexed owner, address indexed spender, uint256 value);
}

// File: contracts/interfaces/ISolidlyV3Factory.sol



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

/// @title The interface for the Solidly V3 Factory
/// @notice The Solidly V3 Factory facilitates creation of Solidly V3 pools and control over the protocol fees
interface ISolidlyV3Factory {
    /// @notice Emitted when the owner of the factory is changed
    /// @param oldOwner The owner before the owner was changed
    /// @param newOwner The owner after the owner was changed
    event OwnerChanged(address indexed oldOwner, address indexed newOwner);

    /// @notice Emitted when the address authorized to collect pool fees is changed
    /// @param oldFeeCollector The fee collector before the change
    /// @param newFeeCollector The fee collector after the change
    event FeeCollectorChanged(address indexed oldFeeCollector, address indexed newFeeCollector);

    /// @notice Emitted when the fee setting auth status of an address is toggled
    /// @param addr The address whose fee setting auth status was toggled
    /// @param newStatus The new fee setting auth status of the address
    event FeeSetterStatusToggled(address indexed addr, uint256 indexed newStatus);

    /// @notice Emitted when a pool is created
    /// @param token0 The first token of the pool by address sort order
    /// @param token1 The second token of the pool by address sort order
    /// @param fee The fee collected upon every swap in the pool, denominated in hundredths of a bip
    /// @param tickSpacing The minimum number of ticks between initialized ticks
    /// @param pool The address of the created pool
    event PoolCreated(
        address indexed token0,
        address indexed token1,
        uint24 fee,
        int24 indexed tickSpacing,
        address pool
    );

    /// @notice Emitted when a new fee amount (and associated tick spacing) is enabled for pool creation via the factory
    /// @param fee The enabled fee, denominated in hundredths of a bip
    /// @param tickSpacing The minimum number of ticks between initialized ticks for pools created with the given fee
    event FeeAmountEnabled(uint24 indexed fee, int24 indexed tickSpacing);

    /// @notice Returns the current owner of the factory
    /// @dev Can be changed by the current owner via setOwner
    /// @return The address of the factory owner
    function owner() external view returns (address);

    /// @notice Returns the current fee collector of the factory
    /// @dev Can be changed by the current owner via setFeeCollector
    /// @return The address of the fee collector
    function feeCollector() external view returns (address);

    /// @notice Returns the fee setting auth status of an address
    /// @dev Can be changed by the current owner via toggleFeeSetterStatus
    /// @return Authorized status as uint (0: authorized to set fees, 1: not authorized to set fees)
    function isFeeSetter(address addr) external view returns (uint256);

    /// @notice Returns the set of addresses that are currently authorized to set pool fees
    /// @dev The underlying set that supports this view is updated every time the isFeeSetter mapping is updated
    /// It's maintained solely to provide an easy on-chain view of all currently authorized addresses
    /// @return Authorized status as uint (0: authorized to set fees, 1: not authorized to set fees)
    function getFeeSetters() external view returns (address[] memory);

    /// @notice Returns the tick spacing for a given fee amount, if enabled, or 0 if not enabled
    /// @dev A fee amount can never be removed, so this value should be hard coded or cached in the calling context
    /// @param fee The enabled fee, denominated in hundredths of a bip. Returns 0 in case of unenabled fee
    /// @return The tick spacing
    function feeAmountTickSpacing(uint24 fee) external view returns (int24);

    /// @notice Returns the pool address for a given pair of tokens and a tick spacing value, or address 0 if it does not exist
    /// @dev tokenA and tokenB may be passed in either token0/token1 or token1/token0 order
    /// @param tokenA The contract address of either token0 or token1
    /// @param tokenB The contract address of the other token
    /// @param tickSpacing The tick spacing value for the pool
    /// @return pool The pool address
    function getPool(address tokenA, address tokenB, int24 tickSpacing) external view returns (address pool);

    /// @notice Creates a pool for the given two tokens and fee
    /// @param tokenA One of the two tokens in the desired pool
    /// @param tokenB The other of the two tokens in the desired pool
    /// @param fee The desired fee for the pool
    /// @dev tokenA and tokenB may be passed in either order: token0/token1 or token1/token0. tickSpacing is retrieved
    /// from the fee. The call will revert if the pool already exists, the fee is invalid, or the token arguments
    /// are invalid.
    /// @dev The pool is uniquely identified by the two tokens and the tick spacing value. The fee is mutable post pool creation.
    /// @return pool The address of the newly created pool
    function createPool(address tokenA, address tokenB, uint24 fee) external returns (address pool);

    /// @notice Updates the owner of the factory
    /// @dev Must be called by the current owner
    /// @param _owner The new owner of the factory
    function setOwner(address _owner) external;

    /// @notice Updates the address that is authorized to collect pool fees
    /// @dev Must be called by the current owner
    /// @param _feeCollector The new fee collector
    function setFeeCollector(address _feeCollector) external;

    /// @notice Toggles the fee setting auth status of the address
    /// @dev Must be called by the current owner
    /// @param addr The address that will have its fee setting auth status toggled
    function toggleFeeSetterStatus(address addr) external;

    /// @notice Enables a fee amount with the given tickSpacing
    /// @dev Fee amounts may never be removed once enabled
    /// @param fee The fee amount to enable, denominated in hundredths of a bip (i.e. 1e-6)
    /// @param tickSpacing The spacing between ticks to be enforced for all pools created with the given fee amount
    function enableFeeAmount(uint24 fee, int24 tickSpacing) external;
}

// File: contracts/interfaces/ISolidlyV3Pool.sol



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

import './pool/ISolidlyV3PoolImmutables.sol';
import './pool/ISolidlyV3PoolState.sol';
import './pool/ISolidlyV3PoolQuoter.sol';
import './pool/ISolidlyV3PoolActions.sol';
import './pool/ISolidlyV3PoolOwnerActions.sol';
import './pool/ISolidlyV3PoolEvents.sol';

/// @title The interface for a Solidly V3 Pool
/// @notice A Solidly 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 ISolidlyV3Pool is
    ISolidlyV3PoolImmutables,
    ISolidlyV3PoolState,
    ISolidlyV3PoolQuoter,
    ISolidlyV3PoolActions,
    ISolidlyV3PoolOwnerActions,
    ISolidlyV3PoolEvents
{

}

// File: contracts/interfaces/ISolidlyV3PoolDeployer.sol



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

/// @title An interface for a contract that is capable of deploying Solidly V3 Pools
/// @notice A contract that constructs a pool must implement this to pass arguments to the pool
/// @dev This is used to avoid having constructor arguments in the pool contract, which results in the init code hash
/// of the pool being constant allowing the CREATE2 address of the pool to be cheaply computed on-chain
interface ISolidlyV3PoolDeployer {
    /// @notice Get the parameters to be used in constructing the pool, set transiently during pool creation.
    /// @dev Called by the pool constructor to fetch the parameters of the pool
    /// Returns factory The factory address
    /// Returns token0 The first token of the pool by address sort order
    /// Returns token1 The second token of the pool by address sort order
    /// Returns fee The fee collected upon every swap in the pool, denominated in hundredths of a bip
    /// Returns tickSpacing The minimum number of ticks between initialized ticks
    function parameters()
        external
        view
        returns (
            address factory,
            address token0,
            address token1,
            uint24 fee,
            int24 tickSpacing
        );
}

// File: contracts/interfaces/pool/ISolidlyV3PoolActions.sol



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

/// @title Permissionless pool actions
/// @notice Contains pool methods that can be called by anyone
interface ISolidlyV3PoolActions {
    /// @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
    /// Minimal (and cheapest) version with no callback or additional slippage/deadline protection
    /// @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
    /// @return amount0 The amount of token0 that was paid to mint the given amount of liquidity
    /// @return amount1 The amount of token1 that was paid to mint the given amount of liquidity
    function mint(
        address recipient,
        int24 tickLower,
        int24 tickUpper,
        uint128 amount
    ) external returns (uint256 amount0, uint256 amount1);

    /// @notice Adds liquidity for the given recipient/tickLower/tickUpper position
    /// Uses callback for payments; no additional slippage/deadline protection
    /// @dev The caller of this method receives a callback in the form of ISolidlyV3MintCallback#solidlyV3MintCallback
    /// in which they must pay any token0 or token1 owed for the liquidity
    /// @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 to 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 Adds liquidity for the given recipient/tickLower/tickUpper position
    /// No callback; includes additional slippage/deadline protection
    /// @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 amount0Min The minimum amount of token0 to spend, which serves as a slippage check
    /// @param amount1Min The minimum amount of token1 to spend, which serves as a slippage check
    /// @param deadline A constraint on the time by which the mint transaction must mined
    /// @return amount0 The amount of token0 that was paid to mint the given amount of liquidity
    /// @return amount1 The amount of token1 that was paid to mint the given amount of liquidity
    function mint(
        address recipient,
        int24 tickLower,
        int24 tickUpper,
        uint128 amount,
        uint256 amount0Min,
        uint256 amount1Min,
        uint256 deadline
    ) external returns (uint256 amount0, uint256 amount1);

    /// @notice Adds liquidity for the given recipient/tickLower/tickUpper position
    /// Uses callback for payments and includes additional slippage/deadline protection
    /// @dev The caller of this method receives a callback in the form of ISolidlyV3MintCallback#solidlyV3MintCallback
    /// in which they must pay any token0 or token1 owed for the liquidity
    /// @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 amount0Min The minimum amount of token0 to spend, which serves as a slippage check
    /// @param amount1Min The minimum amount of token1 to spend, which serves as a slippage check
    /// @param deadline A constraint on the time by which the mint transaction must mined
    /// @param data Any data to 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,
        uint256 amount0Min,
        uint256 amount1Min,
        uint256 deadline,
        bytes calldata data
    ) external returns (uint256 amount0, uint256 amount1);

    /// @notice Convenience method to burn liquidity and then collect owed tokens in one go
    /// @param recipient The address which should receive the tokens collected
    /// @param tickLower The lower tick of the position for which to collect tokens
    /// @param tickUpper The upper tick of the position for which to collect tokens
    /// @param amountToBurn How much liquidity to burn
    /// @param amount0ToCollect How much token0 should be withdrawn from the tokens owed
    /// @param amount1ToCollect How much token1 should be withdrawn from the tokens owed
    /// @return amount0FromBurn The amount of token0 accrued to the position from the burn
    /// @return amount1FromBurn The amount of token1 accrued to the position from the burn
    /// @return amount0Collected The amount of token0 collected from the positions
    /// @return amount1Collected The amount of token1 collected from the positions
    function burnAndCollect(
        address recipient,
        int24 tickLower,
        int24 tickUpper,
        uint128 amountToBurn,
        uint128 amount0ToCollect,
        uint128 amount1ToCollect
    )
        external
        returns (uint256 amount0FromBurn, uint256 amount1FromBurn, uint128 amount0Collected, uint128 amount1Collected);

    /// @notice Convenience method to burn liquidity and then collect owed tokens in one go
    /// Includes additional slippage/deadline protection
    /// @param recipient The address which should receive the tokens collected
    /// @param tickLower The lower tick of the position for which to collect tokens
    /// @param tickUpper The upper tick of the position for which to collect tokens
    /// @param amountToBurn How much liquidity to burn
    /// @param amount0FromBurnMin The minimum amount of token0 that should be accounted for the burned liquidity
    /// @param amount1FromBurnMin The minimum amount of token1 that should be accounted for the burned liquidity
    /// @param amount0ToCollect How much token0 should be withdrawn from the tokens owed
    /// @param amount1ToCollect How much token1 should be withdrawn from the tokens owed
    /// @param deadline A constraint on the time by which the burn transaction must mined
    /// @return amount0FromBurn The amount of token0 accrued to the position from the burn
    /// @return amount1FromBurn The amount of token1 accrued to the position from the burn
    /// @return amount0Collected The amount of token0 collected from the positions
    /// @return amount1Collected The amount of token1 collected from the positions
    function burnAndCollect(
        address recipient,
        int24 tickLower,
        int24 tickUpper,
        uint128 amountToBurn,
        uint256 amount0FromBurnMin,
        uint256 amount1FromBurnMin,
        uint128 amount0ToCollect,
        uint128 amount1ToCollect,
        uint256 deadline
    )
        external
        returns (uint256 amount0FromBurn, uint256 amount1FromBurn, uint128 amount0Collected, uint128 amount1Collected);

    /// @notice Collects tokens owed to a position
    /// @dev Does not recompute tokens earned, which must be done either via mint or burn of any amount of liquidity.
    /// Collect must be called by the position owner. To withdraw only token0 or only token1, amount0Requested or
    /// amount1Requested may be set to zero. To withdraw all tokens owed, caller may pass any value greater than the
    /// actual tokens owed, e.g. type(uint128).max. Tokens owed are from burned liquidity.
    /// @param recipient The address which should receive the tokens collected
    /// @param tickLower The lower tick of the position for which to collect tokens
    /// @param tickUpper The upper tick of the position for which to collect tokens
    /// @param amount0Requested How much token0 should be withdrawn from the tokens owed
    /// @param amount1Requested How much token1 should be withdrawn from the tokens owed
    /// @return amount0 The amount of tokens collected in token0
    /// @return amount1 The amount of tokens 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 Tokens 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 Burn liquidity from the sender and account tokens owed for the liquidity to the position
    /// Includes additional slippage/deadline protection
    /// @dev Tokens 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
    /// @param amount0Min The minimum amount of token0 that should be accounted for the burned liquidity
    /// @param amount1Min The minimum amount of token1 that should be accounted for the burned liquidity
    /// @param deadline A constraint on the time by which the burn transaction must mined
    /// @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,
        uint256 amount0Min,
        uint256 amount1Min,
        uint256 deadline
    ) external returns (uint256 amount0, uint256 amount1);

    /// @notice Swap token0 for token1, or token1 for token0
    /// Minimal (and cheapest) version with no callback, additional slippage/deadline protection, or referrer tracking
    /// @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
    /// @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
    ) external returns (int256 amount0, int256 amount1);

    /// @notice Swap token0 for token1, or token1 for token0
    /// Uses a callback for payments; no additional slippage/deadline protection or referrer tracking
    /// @dev The caller of this method receives a callback in the form of ISolidlyV3MintCallback#solidlyV3SwapCallback
    /// in which they must pay any token0 or token1 owed for the swap
    /// @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 Swap token0 for token1, or token1 for token0
    /// Has additional slippage/deadline protection; no callback or referrer tracking
    /// @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 amountLimit A constraint on the minimum amount out received (for exact input swaps) or maxium amount spent (exact output swaps)
    /// @param deadline A constraint on the time by which the swap transaction must mined
    /// @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,
        uint256 amountLimit,
        uint256 deadline
    ) external returns (int256 amount0, int256 amount1);

    /// @notice Swap token0 for token1, or token1 for token0
    /// Uses a callback for payments and has additional slippage/deadline protection; no referrer tracking
    /// @dev The caller of this method receives a callback in the form of ISolidlyV3MintCallback#solidlyV3SwapCallback
    /// in which they must pay any token0 or token1 owed for the swap
    /// @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 amountLimit A constraint on the minimum amount out received (for exact input swaps) or maxium amount spent (exact output swaps)
    /// @param deadline A constraint on the time by which the swap transaction must mined
    /// @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,
        uint256 amountLimit,
        uint256 deadline,
        bytes calldata data
    ) external returns (int256 amount0, int256 amount1);

    /// @notice Swap token0 for token1, or token1 for token0
    /// Tracks referrers for attribution; No callback or additional slippage/deadline protection
    /// @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 trackingCode Tracking code to be used for referrer attribution
    /// @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,
        uint256 trackingCode
    ) external returns (int256 amount0, int256 amount1);

    /// @notice Swap token0 for token1, or token1 for token0
    /// Tracks referrers for attribution and uses callback for payments; no additional slippage/deadline protection
    /// @dev The caller of this method receives a callback in the form of ISolidlyV3MintCallback#solidlyV3SwapCallback
    /// in which they must pay any token0 or token1 owed for the swap
    /// @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
    /// @param trackingCode Tracking code to be used for referrer attribution
    /// @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,
        uint256 trackingCode
    ) external returns (int256 amount0, int256 amount1);

    /// @notice Swap token0 for token1, or token1 for token0
    /// Tracks referrers for attribution and includes additional slippage/deadline protection; no callback
    /// @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 amountLimit A constraint on the minimum amount out received (for exact input swaps) or maxium amount spent (exact output swaps)
    /// @param deadline A constraint on the time by which the swap transaction must mined
    /// @param trackingCode Tracking code to be used for referrer attribution
    /// @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,
        uint256 amountLimit,
        uint256 deadline,
        uint256 trackingCode
    ) external returns (int256 amount0, int256 amount1);

    /// @notice Swap token0 for token1, or token1 for token0
    /// Tracks referrers for attribution, includes additional slippage/deadline protection, and uses callback for payments
    /// @dev The caller of this method receives a callback in the form of ISolidlyV3MintCallback#solidlyV3SwapCallback
    /// in which they must pay any token0 or token1 owed for the swap
    /// @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 amountLimit A constraint on the minimum amount out received (for exact input swaps) or maxium amount spent (exact output swaps)
    /// @param deadline A constraint on the time by which the swap transaction must mined
    /// @param data Any data to be passed through to the callback
    /// @param trackingCode Tracking code to be used for referrer attribution
    /// @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,
        uint256 amountLimit,
        uint256 deadline,
        bytes calldata data,
        uint256 trackingCode
    ) 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 ISolidlyV3FlashCallback#solidlyV3FlashCallback
    /// @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;
}

// File: contracts/interfaces/pool/ISolidlyV3PoolEvents.sol



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

/// @title Events emitted by a pool
/// @notice Contains all events emitted by the pool
interface ISolidlyV3PoolEvents {
    /// @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
    /// @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 liquidity The liquidity of the pool after the swap
    /// @param tick The log base 1.0001 of price of the pool after the swap
    event Swap(
        address indexed sender,
        address indexed recipient,
        int256 amount0,
        int256 amount1,
        uint160 sqrtPriceX96,
        uint128 liquidity,
        int24 tick
    );

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

    /// @notice Emitted when the fee is changed by the pool
    /// @param feeOld The previous value of the fee
    /// @param feeNew The updated value of the fee
    event SetFee(uint24 feeOld, uint24 feeNew);

    /// @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);
}

// File: contracts/interfaces/pool/ISolidlyV3PoolImmutables.sol



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

/// @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 ISolidlyV3PoolImmutables {
    /// @notice The contract that deployed the pool, which must adhere to the ISolidlyV3Factory interface
    /// @return The contract address
    function factory() external view returns (address);

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

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

    /// @notice The pool tick spacing
    /// @dev Ticks can only be used at multiples of this value, 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);
}

// File: contracts/interfaces/pool/ISolidlyV3PoolOwnerActions.sol



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

/// @title Permissioned pool actions
/// @notice Contains pool methods that may only be called by the factory owner
interface ISolidlyV3PoolOwnerActions {
    /// @notice Set the pool's trading fee (applied to input tokens on all swaps)
    /// @param fee new trading fee in hundredths of a bip, i.e. 1e-6
    function setFee(uint24 fee) external;

    /// @notice Collect the protocol fee accrued to the pool. All fees are to be collected only by
    /// the protocol's Reward Distributor, which processes claims for liquidity providers and protocol
    /// voters after verifying them against a periodically updated merkle root
    /// @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);
}

// File: contracts/interfaces/pool/ISolidlyV3PoolQuoter.sol



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

/// @title Quoter Interface
/// @notice Supports quoting the calculated amounts and resulting pool state from swaps
interface ISolidlyV3PoolQuoter {
    /// @notice Returns the amounts in/out and resulting pool state for a swap without executing 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
    /// @return amount0 The delta of the pool's balance of token0 that will result from the swap (exact when negative, minimum when positive)
    /// @return amount1 The delta of the pool's balance of token1 that will result from the swap (exact when negative, minimum when positive)
    /// @return sqrtPriceX96After The value the pool's sqrtPriceX96 will have after the swap
    /// @return tickAfter The value the pool's tick will have after the swap
    /// @return liquidityAfter The value the pool's liquidity will have after the swap
    function quoteSwap(
        bool zeroForOne,
        int256 amountSpecified,
        uint160 sqrtPriceLimitX96
    )
        external
        view
        returns (int256 amount0, int256 amount1, uint160 sqrtPriceX96After, int24 tickAfter, uint128 liquidityAfter);
}

// File: contracts/interfaces/pool/ISolidlyV3PoolState.sol



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

/// @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 ISolidlyV3PoolState {
    /// @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.
    /// fee The pool's current fee in hundredths of a bip, i.e. 1e-6
    /// unlocked Whether the pool is currently locked to reentrancy
    function slot0() external view returns (uint160 sqrtPriceX96, int24 tick, uint24 fee, bool unlocked);

    /// @notice The amounts of token0 and token1 that have accrued as pool fees
    /// @dev Pool fees will never exceed uint128 max in either token
    function poolFees() 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,
    /// initialized Set to true if the tick is initialized, i.e. liquidityGross is greater than 0, otherwise equal to false.
    /// Outside 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 must be used only in comparison to previous snapshots for
    /// a specific position.
    function ticks(int24 tick) external view returns (uint128 liquidityGross, int128 liquidityNet, bool initialized);

    /// @notice Returns 256 packed tick initialized boolean values. See TickBitmap for more information
    function tickBitmap(int16 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 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, uint128 tokensOwed0, uint128 tokensOwed1);
}

// File: contracts/libraries/BitMath.sol



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

/// @title BitMath
/// @dev This library provides functionality for computing bit properties of an unsigned integer
library BitMath {
    /// @notice Returns the index of the most significant bit of the number,
    ///     where the least significant bit is at index 0 and the most significant bit is at index 255
    /// @dev The function satisfies the property:
    ///     x >= 2**mostSignificantBit(x) and x < 2**(mostSignificantBit(x)+1)
    /// @param x the value for which to compute the most significant bit, must be greater than 0
    /// @return r the index of the most significant bit
    function mostSignificantBit(uint256 x) internal pure returns (uint8 r) {
        require(x > 0);

        if (x >= 0x100000000000000000000000000000000) {
            x >>= 128;
            r += 128;
        }
        if (x >= 0x10000000000000000) {
            x >>= 64;
            r += 64;
        }
        if (x >= 0x100000000) {
            x >>= 32;
            r += 32;
        }
        if (x >= 0x10000) {
            x >>= 16;
            r += 16;
        }
        if (x >= 0x100) {
            x >>= 8;
            r += 8;
        }
        if (x >= 0x10) {
            x >>= 4;
            r += 4;
        }
        if (x >= 0x4) {
            x >>= 2;
            r += 2;
        }
        if (x >= 0x2) r += 1;
    }

    /// @notice Returns the index of the least significant bit of the number,
    ///     where the least significant bit is at index 0 and the most significant bit is at index 255
    /// @dev The function satisfies the property:
    ///     (x & 2**leastSignificantBit(x)) != 0 and (x & (2**(leastSignificantBit(x)) - 1)) == 0)
    /// @param x the value for which to compute the least significant bit, must be greater than 0
    /// @return r the index of the least significant bit
    function leastSignificantBit(uint256 x) internal pure returns (uint8 r) {
        require(x > 0);

        r = 255;
        if (x & type(uint128).max > 0) {
            r -= 128;
        } else {
            x >>= 128;
        }
        if (x & type(uint64).max > 0) {
            r -= 64;
        } else {
            x >>= 64;
        }
        if (x & type(uint32).max > 0) {
            r -= 32;
        } else {
            x >>= 32;
        }
        if (x & type(uint16).max > 0) {
            r -= 16;
        } else {
            x >>= 16;
        }
        if (x & type(uint8).max > 0) {
            r -= 8;
        } else {
            x >>= 8;
        }
        if (x & 0xf > 0) {
            r -= 4;
        } else {
            x >>= 4;
        }
        if (x & 0x3 > 0) {
            r -= 2;
        } else {
            x >>= 2;
        }
        if (x & 0x1 > 0) r -= 1;
    }
}

// File: contracts/libraries/FixedPoint128.sol



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

/// @title FixedPoint128
/// @notice A library for handling binary fixed point numbers, see https://en.wikipedia.org/wiki/Q_(number_format)
library FixedPoint128 {
    uint256 internal constant Q128 = 0x100000000000000000000000000000000;
}

// File: contracts/libraries/FixedPoint96.sol



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

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

// File: contracts/libraries/FullMath.sol



// SPDX-License-Identifier: MIT
pragma solidity >=0.4.0 <0.8.0;

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

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

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

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

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

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

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

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

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

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

// File: contracts/libraries/LiquidityMath.sol



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

/// @title Math library for liquidity
library LiquidityMath {
    /// @notice Add a signed liquidity delta to liquidity and revert if it overflows or underflows
    /// @param x The liquidity before change
    /// @param y The delta by which liquidity should be changed
    /// @return z The liquidity delta
    function addDelta(uint128 x, int128 y) internal pure returns (uint128 z) {
        if (y < 0) {
            require((z = x - uint128(-y)) < x, 'LS');
        } else {
            require((z = x + uint128(y)) >= x, 'LA');
        }
    }
}

// File: contracts/libraries/LowGasSafeMath.sol



// SPDX-License-Identifier: GPL-2.0-or-later
pragma solidity >=0.7.0;

/// @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));
    }
}

// File: contracts/libraries/Position.sol



// SPDX-License-Identifier: GPL-2.0-or-later
pragma solidity >=0.5.0 <0.8.0;

import './FullMath.sol';
import './FixedPoint128.sol';
import './LiquidityMath.sol';

/// @title Position
/// @notice Positions represent an owner address' liquidity between a lower and upper tick boundary
/// @dev Positions store additional state for tracking tokens owed to the position
library Position {
    // info stored for each user's position
    struct Info {
        // the amount of liquidity owned by this position
        uint128 liquidity;
        // the tokens owed to the position owner in token0/token1
        uint128 tokensOwed0;
        uint128 tokensOwed1;
    }

    /// @notice Returns the Info struct of a position, given an owner and position boundaries
    /// @param self The mapping containing all user positions
    /// @param owner The address of the position owner
    /// @param tickLower The lower tick boundary of the position
    /// @param tickUpper The upper tick boundary of the position
    /// @return position The position info struct of the given owners' position
    function get(
        mapping(bytes32 => Info) storage self,
        address owner,
        int24 tickLower,
        int24 tickUpper
    ) internal view returns (Position.Info storage position) {
        position = self[keccak256(abi.encodePacked(owner, tickLower, tickUpper))];
    }

    /// @notice Updates the liquidity amount associated with a user's position
    /// @param self The individual position to update
    /// @param liquidityDelta The change in pool liquidity as a result of the position update
    function update(Info storage self, int128 liquidityDelta) internal {
        if (liquidityDelta != 0) {
            self.liquidity = LiquidityMath.addDelta(self.liquidity, liquidityDelta);
        }
    }
}

// File: contracts/libraries/SafeCast.sol



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

/// @title Safe casting methods
/// @notice Contains methods for safely casting between types
library SafeCast {
    /// @notice Cast a uint256 to a uint160, revert on overflow
    /// @param y The uint256 to be downcasted
    /// @return z The downcasted integer, now type uint160
    function toUint160(uint256 y) internal pure returns (uint160 z) {
        require((z = uint160(y)) == y);
    }

    /// @notice Cast a int256 to a int128, revert on overflow or underflow
    /// @param y The int256 to be downcasted
    /// @return z The downcasted integer, now type int128
    function toInt128(int256 y) internal pure returns (int128 z) {
        require((z = int128(y)) == y);
    }

    /// @notice Cast a uint256 to a int256, revert on overflow
    /// @param y The uint256 to be casted
    /// @return z The casted integer, now type int256
    function toInt256(uint256 y) internal pure returns (int256 z) {
        require(y < 2**255);
        z = int256(y);
    }
}

// File: contracts/libraries/SqrtPriceMath.sol



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

import './LowGasSafeMath.sol';
import './SafeCast.sol';

import './FullMath.sol';
import './UnsafeMath.sol';
import './FixedPoint96.sol';

/// @title Functions based on Q64.96 sqrt price and liquidity
/// @notice Contains the math that uses square root of price as a Q64.96 and liquidity to compute deltas
library SqrtPriceMath {
    using LowGasSafeMath for uint256;
    using SafeCast for uint256;

    /// @notice Gets the next sqrt price given a delta of token0
    /// @dev Always rounds up, because in the exact output case (increasing price) we need to move the price at least
    /// far enough to get the desired output amount, and in the exact input case (decreasing price) we need to move the
    /// price less in order to not send too much output.
    /// The most precise formula for this is liquidity * sqrtPX96 / (liquidity +- amount * sqrtPX96),
    /// if this is impossible because of overflow, we calculate liquidity / (liquidity / sqrtPX96 +- amount).
    /// @param sqrtPX96 The starting price, i.e. before accounting for the token0 delta
    /// @param liquidity The amount of usable liquidity
    /// @param amount How much of token0 to add or remove from virtual reserves
    /// @param add Whether to add or remove the amount of token0
    /// @return The price after adding or removing amount, depending on add
    function getNextSqrtPriceFromAmount0RoundingUp(
        uint160 sqrtPX96,
        uint128 liquidity,
        uint256 amount,
        bool add
    ) internal pure returns (uint160) {
        // we short circuit amount == 0 because the result is otherwise not guaranteed to equal the input price
        if (amount == 0) return sqrtPX96;
        uint256 numerator1 = uint256(liquidity) << FixedPoint96.RESOLUTION;

        if (add) {
            uint256 product;
            if ((product = amount * sqrtPX96) / amount == sqrtPX96) {
                uint256 denominator = numerator1 + product;
                if (denominator >= numerator1)
                    // always fits in 160 bits
                    return uint160(FullMath.mulDivRoundingUp(numerator1, sqrtPX96, denominator));
            }

            return uint160(UnsafeMath.divRoundingUp(numerator1, (numerator1 / sqrtPX96).add(amount)));
        } else {
            uint256 product;
            // if the product overflows, we know the denominator underflows
            // in addition, we must check that the denominator does not underflow
            require((product = amount * sqrtPX96) / amount == sqrtPX96 && numerator1 > product);
            uint256 denominator = numerator1 - product;
            return FullMath.mulDivRoundingUp(numerator1, sqrtPX96, denominator).toUint160();
        }
    }

    /// @notice Gets the next sqrt price given a delta of token1
    /// @dev Always rounds down, because in the exact output case (decreasing price) we need to move the price at least
    /// far enough to get the desired output amount, and in the exact input case (increasing price) we need to move the
    /// price less in order to not send too much output.
    /// The formula we compute is within <1 wei of the lossless version: sqrtPX96 +- amount / liquidity
    /// @param sqrtPX96 The starting price, i.e., before accounting for the token1 delta
    /// @param liquidity The amount of usable liquidity
    /// @param amount How much of token1 to add, or remove, from virtual reserves
    /// @param add Whether to add, or remove, the amount of token1
    /// @return The price after adding or removing `amount`
    function getNextSqrtPriceFromAmount1RoundingDown(
        uint160 sqrtPX96,
        uint128 liquidity,
        uint256 amount,
        bool add
    ) internal pure returns (uint160) {
        // if we're adding (subtracting), rounding down requires rounding the quotient down (up)
        // in both cases, avoid a mulDiv for most inputs
        if (add) {
            uint256 quotient =
                (
                    amount <= type(uint160).max
                        ? (amount << FixedPoint96.RESOLUTION) / liquidity
                        : FullMath.mulDiv(amount, FixedPoint96.Q96, liquidity)
                );

            return uint256(sqrtPX96).add(quotient).toUint160();
        } else {
            uint256 quotient =
                (
                    amount <= type(uint160).max
                        ? UnsafeMath.divRoundingUp(amount << FixedPoint96.RESOLUTION, liquidity)
                        : FullMath.mulDivRoundingUp(amount, FixedPoint96.Q96, liquidity)
                );

            require(sqrtPX96 > quotient);
            // always fits 160 bits
            return uint160(sqrtPX96 - quotient);
        }
    }

    /// @notice Gets the next sqrt price given an input amount of token0 or token1
    /// @dev Throws if price or liquidity are 0, or if the next price is out of bounds
    /// @param sqrtPX96 The starting price, i.e., before accounting for the input amount
    /// @param liquidity The amount of usable liquidity
    /// @param amountIn How much of token0, or token1, is being swapped in
    /// @param zeroForOne Whether the amount in is token0 or token1
    /// @return sqrtQX96 The price after adding the input amount to token0 or token1
    function getNextSqrtPriceFromInput(
        uint160 sqrtPX96,
        uint128 liquidity,
        uint256 amountIn,
        bool zeroForOne
    ) internal pure returns (uint160 sqrtQX96) {
        require(sqrtPX96 > 0);
        require(liquidity > 0);

        // round to make sure that we don't pass the target price
        return
            zeroForOne
                ? getNextSqrtPriceFromAmount0RoundingUp(sqrtPX96, liquidity, amountIn, true)
                : getNextSqrtPriceFromAmount1RoundingDown(sqrtPX96, liquidity, amountIn, true);
    }

    /// @notice Gets the next sqrt price given an output amount of token0 or token1
    /// @dev Throws if price or liquidity are 0 or the next price is out of bounds
    /// @param sqrtPX96 The starting price before accounting for the output amount
    /// @param liquidity The amount of usable liquidity
    /// @param amountOut How much of token0, or token1, is being swapped out
    /// @param zeroForOne Whether the amount out is token0 or token1
    /// @return sqrtQX96 The price after removing the output amount of token0 or token1
    function getNextSqrtPriceFromOutput(
        uint160 sqrtPX96,
        uint128 liquidity,
        uint256 amountOut,
        bool zeroForOne
    ) internal pure returns (uint160 sqrtQX96) {
        require(sqrtPX96 > 0);
        require(liquidity > 0);

        // round to make sure that we pass the target price
        return
            zeroForOne
                ? getNextSqrtPriceFromAmount1RoundingDown(sqrtPX96, liquidity, amountOut, false)
                : getNextSqrtPriceFromAmount0RoundingUp(sqrtPX96, liquidity, amountOut, false);
    }

    /// @notice Gets the amount0 delta between two prices
    /// @dev Calculates liquidity / sqrt(lower) - liquidity / sqrt(upper),
    /// i.e. liquidity * (sqrt(upper) - sqrt(lower)) / (sqrt(upper) * sqrt(lower))
    /// @param sqrtRatioAX96 A sqrt price
    /// @param sqrtRatioBX96 Another sqrt price
    /// @param liquidity The amount of usable liquidity
    /// @param roundUp Whether to round the amount up or down
    /// @return amount0 Amount of token0 required to cover a position of size liquidity between the two passed prices
    function getAmount0Delta(
        uint160 sqrtRatioAX96,
        uint160 sqrtRatioBX96,
        uint128 liquidity,
        bool roundUp
    ) internal pure returns (uint256 amount0) {
        if (sqrtRatioAX96 > sqrtRatioBX96) (sqrtRatioAX96, sqrtRatioBX96) = (sqrtRatioBX96, sqrtRatioAX96);

        uint256 numerator1 = uint256(liquidity) << FixedPoint96.RESOLUTION;
        uint256 numerator2 = sqrtRatioBX96 - sqrtRatioAX96;

        require(sqrtRatioAX96 > 0);

        return
            roundUp
                ? UnsafeMath.divRoundingUp(
                    FullMath.mulDivRoundingUp(numerator1, numerator2, sqrtRatioBX96),
                    sqrtRatioAX96
                )
                : FullMath.mulDiv(numerator1, numerator2, sqrtRatioBX96) / sqrtRatioAX96;
    }

    /// @notice Gets the amount1 delta between two prices
    /// @dev Calculates liquidity * (sqrt(upper) - sqrt(lower))
    /// @param sqrtRatioAX96 A sqrt price
    /// @param sqrtRatioBX96 Another sqrt price
    /// @param liquidity The amount of usable liquidity
    /// @param roundUp Whether to round the amount up, or down
    /// @return amount1 Amount of token1 required to cover a position of size liquidity between the two passed prices
    function getAmount1Delta(
        uint160 sqrtRatioAX96,
        uint160 sqrtRatioBX96,
        uint128 liquidity,
        bool roundUp
    ) internal pure returns (uint256 amount1) {
        if (sqrtRatioAX96 > sqrtRatioBX96) (sqrtRatioAX96, sqrtRatioBX96) = (sqrtRatioBX96, sqrtRatioAX96);

        return
            roundUp
                ? FullMath.mulDivRoundingUp(liquidity, sqrtRatioBX96 - sqrtRatioAX96, FixedPoint96.Q96)
                : FullMath.mulDiv(liquidity, sqrtRatioBX96 - sqrtRatioAX96, FixedPoint96.Q96);
    }

    /// @notice Helper that gets signed token0 delta
    /// @param sqrtRatioAX96 A sqrt price
    /// @param sqrtRatioBX96 Another sqrt price
    /// @param liquidity The change in liquidity for which to compute the amount0 delta
    /// @return amount0 Amount of token0 corresponding to the passed liquidityDelta between the two prices
    function getAmount0Delta(
        uint160 sqrtRatioAX96,
        uint160 sqrtRatioBX96,
        int128 liquidity
    ) internal pure returns (int256 amount0) {
        return
            liquidity < 0
                ? -getAmount0Delta(sqrtRatioAX96, sqrtRatioBX96, uint128(-liquidity), false).toInt256()
                : getAmount0Delta(sqrtRatioAX96, sqrtRatioBX96, uint128(liquidity), true).toInt256();
    }

    /// @notice Helper that gets signed token1 delta
    /// @param sqrtRatioAX96 A sqrt price
    /// @param sqrtRatioBX96 Another sqrt price
    /// @param liquidity The change in liquidity for which to compute the amount1 delta
    /// @return amount1 Amount of token1 corresponding to the passed liquidityDelta between the two prices
    function getAmount1Delta(
        uint160 sqrtRatioAX96,
        uint160 sqrtRatioBX96,
        int128 liquidity
    ) internal pure returns (int256 amount1) {
        return
            liquidity < 0
                ? -getAmount1Delta(sqrtRatioAX96, sqrtRatioBX96, uint128(-liquidity), false).toInt256()
                : getAmount1Delta(sqrtRatioAX96, sqrtRatioBX96, uint128(liquidity), true).toInt256();
    }
}

// File: contracts/libraries/SwapMath.sol



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

import './FullMath.sol';
import './SqrtPriceMath.sol';

/// @title Computes the result of a swap within ticks
/// @notice Contains methods for computing the result of a swap within a single tick price range, i.e., a single tick.
library SwapMath {
    /// @notice Computes the result of swapping some amount in, or amount out, given the parameters of the swap
    /// @dev The fee, plus the amount in, will never exceed the amount remaining if the swap's `amountSpecified` is positive
    /// @param sqrtRatioCurrentX96 The current sqrt price of the pool
    /// @param sqrtRatioTargetX96 The price that cannot be exceeded, from which the direction of the swap is inferred
    /// @param liquidity The usable liquidity
    /// @param amountRemaining How much input or output amount is remaining to be swapped in/out
    /// @param feePips The fee taken from the input amount, expressed in hundredths of a bip
    /// @return sqrtRatioNextX96 The price after swapping the amount in/out, not to exceed the price target
    /// @return amountIn The amount to be swapped in, of either token0 or token1, based on the direction of the swap
    /// @return amountOut The amount to be received, of either token0 or token1, based on the direction of the swap
    /// @return feeAmount The amount of input that will be taken as a fee
    function computeSwapStep(
        uint160 sqrtRatioCurrentX96,
        uint160 sqrtRatioTargetX96,
        uint128 liquidity,
        int256 amountRemaining,
        uint24 feePips
    )
        internal
        pure
        returns (
            uint160 sqrtRatioNextX96,
            uint256 amountIn,
            uint256 amountOut,
            uint256 feeAmount
        )
    {
        bool zeroForOne = sqrtRatioCurrentX96 >= sqrtRatioTargetX96;
        bool exactIn = amountRemaining >= 0;

        if (exactIn) {
            uint256 amountRemainingLessFee = FullMath.mulDiv(uint256(amountRemaining), 1e6 - feePips, 1e6);
            amountIn = zeroForOne
                ? SqrtPriceMath.getAmount0Delta(sqrtRatioTargetX96, sqrtRatioCurrentX96, liquidity, true)
                : SqrtPriceMath.getAmount1Delta(sqrtRatioCurrentX96, sqrtRatioTargetX96, liquidity, true);
            if (amountRemainingLessFee >= amountIn) sqrtRatioNextX96 = sqrtRatioTargetX96;
            else
                sqrtRatioNextX96 = SqrtPriceMath.getNextSqrtPriceFromInput(
                    sqrtRatioCurrentX96,
                    liquidity,
                    amountRemainingLessFee,
                    zeroForOne
                );
        } else {
            amountOut = zeroForOne
                ? SqrtPriceMath.getAmount1Delta(sqrtRatioTargetX96, sqrtRatioCurrentX96, liquidity, false)
                : SqrtPriceMath.getAmount0Delta(sqrtRatioCurrentX96, sqrtRatioTargetX96, liquidity, false);
            if (uint256(-amountRemaining) >= amountOut) sqrtRatioNextX96 = sqrtRatioTargetX96;
            else
                sqrtRatioNextX96 = SqrtPriceMath.getNextSqrtPriceFromOutput(
                    sqrtRatioCurrentX96,
                    liquidity,
                    uint256(-amountRemaining),
                    zeroForOne
                );
        }

        bool max = sqrtRatioTargetX96 == sqrtRatioNextX96;

        // get the input/output amounts
        if (zeroForOne) {
            amountIn = max && exactIn
                ? amountIn
                : SqrtPriceMath.getAmount0Delta(sqrtRatioNextX96, sqrtRatioCurrentX96, liquidity, true);
            amountOut = max && !exactIn
                ? amountOut
                : SqrtPriceMath.getAmount1Delta(sqrtRatioNextX96, sqrtRatioCurrentX96, liquidity, false);
        } else {
            amountIn = max && exactIn
                ? amountIn
                : SqrtPriceMath.getAmount1Delta(sqrtRatioCurrentX96, sqrtRatioNextX96, liquidity, true);
            amountOut = max && !exactIn
                ? amountOut
                : SqrtPriceMath.getAmount0Delta(sqrtRatioCurrentX96, sqrtRatioNextX96, liquidity, false);
        }

        // cap the output amount to not exceed the remaining output amount
        if (!exactIn && amountOut > uint256(-amountRemaining)) {
            amountOut = uint256(-amountRemaining);
        }

        if (exactIn && sqrtRatioNextX96 != sqrtRatioTargetX96) {
            // we didn't reach the target, so take the remainder of the maximum input as fee
            feeAmount = uint256(amountRemaining) - amountIn;
        } else {
            feeAmount = FullMath.mulDivRoundingUp(amountIn, feePips, 1e6 - feePips);
        }
    }
}

// File: contracts/libraries/Tick.sol



// SPDX-License-Identifier: GPL-2.0-or-later
pragma solidity >=0.5.0 <0.8.0;

import './LowGasSafeMath.sol';
import './SafeCast.sol';

import './TickMath.sol';
import './LiquidityMath.sol';

/// @title Tick
/// @notice Contains functions for managing tick processes and relevant calculations
library Tick {
    using LowGasSafeMath for int256;
    using SafeCast for int256;

    // info stored for each initialized individual tick
    struct Info {
        // the total position liquidity that references this tick
        uint128 liquidityGross;
        // amount of net liquidity added (subtracted) when tick is crossed from left to right (right to left),
        int128 liquidityNet;
        // true iff the tick is initialized, i.e. the value is exactly equivalent to the expression liquidityGross != 0
        // these 8 bits are set to prevent fresh sstores when crossing newly initialized ticks
        bool initialized;
    }

    /// @notice Derives max liquidity per tick from given tick spacing
    /// @dev Executed within the pool constructor
    /// @param tickSpacing The amount of required tick separation, realized in multiples of `tickSpacing`
    ///     e.g., a tickSpacing of 3 requires ticks to be initialized every 3rd tick i.e., ..., -6, -3, 0, 3, 6, ...
    /// @return The max liquidity per tick
    function tickSpacingToMaxLiquidityPerTick(int24 tickSpacing) internal pure returns (uint128) {
        int24 minTick = (TickMath.MIN_TICK / tickSpacing) * tickSpacing;
        int24 maxTick = (TickMath.MAX_TICK / tickSpacing) * tickSpacing;
        uint24 numTicks = uint24((maxTick - minTick) / tickSpacing) + 1;
        return type(uint128).max / numTicks;
    }

    /// @notice Updates a tick and returns true if the tick was flipped from initialized to uninitialized, or vice versa
    /// @param self The mapping containing all tick information for initialized ticks
    /// @param tick The tick that will be updated
    /// @param liquidityDelta A new amount of liquidity to be added (subtracted) when tick is crossed from left to right (right to left)
    /// @param upper true for updating a position's upper tick, or false for updating a position's lower tick
    /// @param maxLiquidity The maximum liquidity allocation for a single tick
    /// @return flipped Whether the tick was flipped from initialized to uninitialized, or vice versa
    function update(
        mapping(int24 => Tick.Info) storage self,
        int24 tick,
        int128 liquidityDelta,
        bool upper,
        uint128 maxLiquidity
    ) internal returns (bool flipped) {
        Tick.Info storage info = self[tick];

        uint128 liquidityGrossBefore = info.liquidityGross;
        uint128 liquidityGrossAfter = LiquidityMath.addDelta(liquidityGrossBefore, liquidityDelta);

        require(liquidityGrossAfter <= maxLiquidity, 'LO');

        flipped = (liquidityGrossAfter == 0) != (liquidityGrossBefore == 0);

        if (liquidityGrossBefore == 0) info.initialized = true;

        info.liquidityGross = liquidityGrossAfter;

        // when the lower (upper) tick is crossed left to right (right to left), liquidity must be added (removed)
        info.liquidityNet = upper
            ? int256(info.liquidityNet).sub(liquidityDelta).toInt128()
            : int256(info.liquidityNet).add(liquidityDelta).toInt128();
    }

    /// @notice Clears tick data
    /// @param self The mapping containing all initialized tick information for initialized ticks
    /// @param tick The tick that will be cleared
    function clear(mapping(int24 => Tick.Info) storage self, int24 tick) internal {
        delete self[tick];
    }

    /// @notice Transitions to next tick as needed by price movement
    /// @param self The mapping containing all tick information for initialized ticks
    /// @param tick The destination tick of the transition
    /// @return liquidityNet The amount of liquidity added (subtracted) when tick is crossed from left to right (right to left)
    function cross(mapping(int24 => Tick.Info) storage self, int24 tick) internal view returns (int128 liquidityNet) {
        liquidityNet = self[tick].liquidityNet;
    }
}

// File: contracts/libraries/TickBitmap.sol



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

import './BitMath.sol';

/// @title Packed tick initialized state library
/// @notice Stores a packed mapping of tick index to its initialized state
/// @dev The mapping uses int16 for keys since ticks are represented as int24 and there are 256 (2^8) values per word.
library TickBitmap {
    /// @notice Computes the position in the mapping where the initialized bit for a tick lives
    /// @param tick The tick for which to compute the position
    /// @return wordPos The key in the mapping containing the word in which the bit is stored
    /// @return bitPos The bit position in the word where the flag is stored
    function position(int24 tick) private pure returns (int16 wordPos, uint8 bitPos) {
        wordPos = int16(tick >> 8);
        bitPos = uint8(tick % 256);
    }

    /// @notice Flips the initialized state for a given tick from false to true, or vice versa
    /// @param self The mapping in which to flip the tick
    /// @param tick The tick to flip
    /// @param tickSpacing The spacing between usable ticks
    function flipTick(
        mapping(int16 => uint256) storage self,
        int24 tick,
        int24 tickSpacing
    ) internal {
        require(tick % tickSpacing == 0); // ensure that the tick is spaced
        (int16 wordPos, uint8 bitPos) = position(tick / tickSpacing);
        uint256 mask = 1 << bitPos;
        self[wordPos] ^= mask;
    }

    /// @notice Returns the next initialized tick contained in the same word (or adjacent word) as the tick that is either
    /// to the left (less than or equal to) or right (greater than) of the given tick
    /// @param self The mapping in which to compute the next initialized tick
    /// @param tick The starting tick
    /// @param tickSpacing The spacing between usable ticks
    /// @param lte Whether to search for the next initialized tick to the left (less than or equal to the starting tick)
    /// @return next The next initialized or uninitialized tick up to 256 ticks away from the current tick
    /// @return initialized Whether the next tick is initialized, as the function only searches within up to 256 ticks
    function nextInitializedTickWithinOneWord(
        mapping(int16 => uint256) storage self,
        int24 tick,
        int24 tickSpacing,
        bool lte
    ) internal view returns (int24 next, bool initialized) {
        int24 compressed = tick / tickSpacing;
        if (tick < 0 && tick % tickSpacing != 0) compressed--; // round towards negative infinity

        if (lte) {
            (int16 wordPos, uint8 bitPos) = position(compressed);
            // all the 1s at or to the right of the current bitPos
            uint256 mask = (1 << bitPos) - 1 + (1 << bitPos);
            uint256 masked = self[wordPos] & mask;

            // if there are no initialized ticks to the right of or at the current tick, return rightmost in the word
            initialized = masked != 0;
            // overflow/underflow is possible, but prevented externally by limiting both tickSpacing and tick
            next = initialized
                ? (compressed - int24(bitPos - BitMath.mostSignificantBit(masked))) * tickSpacing
                : (compressed - int24(bitPos)) * tickSpacing;
        } else {
            // start from the word of the next tick, since the current tick state doesn't matter
            (int16 wordPos, uint8 bitPos) = position(compressed + 1);
            // all the 1s at or to the left of the bitPos
            uint256 mask = ~((1 << bitPos) - 1);
            uint256 masked = self[wordPos] & mask;

            // if there are no initialized ticks to the left of the current tick, return leftmost in the word
            initialized = masked != 0;
            // overflow/underflow is possible, but prevented externally by limiting both tickSpacing and tick
            next = initialized
                ? (compressed + 1 + int24(BitMath.leastSignificantBit(masked) - bitPos)) * tickSpacing
                : (compressed + 1 + int24(type(uint8).max - bitPos)) * tickSpacing;
        }
    }
}

// File: contracts/libraries/TickMath.sol



// SPDX-License-Identifier: GPL-2.0-or-later
pragma solidity >=0.5.0 <0.8.0;

/// @title Math library for computing sqrt prices from ticks and vice versa
/// @notice Computes sqrt price for ticks of size 1.0001, i.e. sqrt(1.0001^tick) as fixed point Q64.96 numbers. Supports
/// prices between 2**-128 and 2**128
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 = type(uint256).max / ratio;

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

// File: contracts/libraries/TransferHelper.sol



// SPDX-License-Identifier: GPL-2.0-or-later
pragma solidity >=0.6.0;

import '../interfaces/IERC20Minimal.sol';

/// @title TransferHelper
/// @notice Contains helper methods for interacting with ERC20 tokens that do not consistently return true/false
library TransferHelper {
    /// @notice Transfers tokens from the targeted address to the given destination
    /// @notice Errors with 'TF' if transfer fails
    /// @param token The contract address of the token to be transferred
    /// @param from The originating address from which the tokens will be transferred
    /// @param to The destination address of the transfer
    /// @param value The amount to be transferred
    function safeTransferFrom(address token, address from, address to, uint256 value) internal {
        (bool success, bytes memory data) = token.call(
            abi.encodeWithSelector(IERC20Minimal.transferFrom.selector, from, to, value)
        );
        require(success && (data.length == 0 || abi.decode(data, (bool))), 'TF');
    }

    /// @notice Transfers tokens from msg.sender to a recipient
    /// @dev Calls transfer on token contract, errors with TF if transfer fails
    /// @param token The contract address of the token which will be transferred
    /// @param to The recipient of the transfer
    /// @param value The value of the transfer
    function safeTransfer(address token, address to, uint256 value) internal {
        (bool success, bytes memory data) = token.call(
            abi.encodeWithSelector(IERC20Minimal.transfer.selector, to, value)
        );
        require(success && (data.length == 0 || abi.decode(data, (bool))), 'TF');
    }
}

// File: contracts/libraries/UnsafeMath.sol



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

/// @title Math functions that do not check inputs or outputs
/// @notice Contains methods that perform common math functions but do not do any overflow or underflow checks
library UnsafeMath {
    /// @notice Returns ceil(x / y)
    /// @dev division by 0 has unspecified behavior, and must be checked externally
    /// @param x The dividend
    /// @param y The divisor
    /// @return z The quotient, ceil(x / y)
    function divRoundingUp(uint256 x, uint256 y) internal pure returns (uint256 z) {
        assembly {
            z := add(div(x, y), gt(mod(x, y), 0))
        }
    }
}

// File: contracts/libraries/Validation.sol



// SPDX-License-Identifier: GPL-2.0-or-later
pragma solidity >=0.5.0 <0.8.0;

abstract contract Validation {
    modifier checkDeadline(uint256 deadline) {
        require(block.timestamp <= deadline, 'TO');
        _;
    }
}

// File: contracts/SolidlyV3Pool.sol



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

import './interfaces/ISolidlyV3Pool.sol';

import './libraries/LowGasSafeMath.sol';
import './libraries/SafeCast.sol';
import './libraries/Tick.sol';
import './libraries/TickBitmap.sol';
import './libraries/Position.sol';
import './libraries/Validation.sol';

import './libraries/FullMath.sol';
import './libraries/FixedPoint128.sol';
import './libraries/TransferHelper.sol';
import './libraries/TickMath.sol';
import './libraries/LiquidityMath.sol';
import './libraries/SqrtPriceMath.sol';
import './libraries/SwapMath.sol';

import './interfaces/ISolidlyV3PoolDeployer.sol';
import './interfaces/ISolidlyV3Factory.sol';
import './interfaces/IERC20Minimal.sol';
import './interfaces/callback/ISolidlyV3SwapCallback.sol';
import './interfaces/callback/ISolidlyV3MintCallback.sol';
import './interfaces/callback/ISolidlyV3FlashCallback.sol';

contract SolidlyV3Pool is ISolidlyV3Pool, Validation {
    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;

    /// @inheritdoc ISolidlyV3PoolImmutables
    address public immutable override factory;
    /// @inheritdoc ISolidlyV3PoolImmutables
    address public immutable override token0;
    /// @inheritdoc ISolidlyV3PoolImmutables
    address public immutable override token1;

    /// @inheritdoc ISolidlyV3PoolImmutables
    int24 public immutable override tickSpacing;

    /// @inheritdoc ISolidlyV3PoolImmutables
    uint128 public immutable override maxLiquidityPerTick;

    struct Slot0 {
        // the current price
        uint160 sqrtPriceX96;
        // the current tick
        int24 tick;
        // the pool's current fee in hundredths of a bip, i.e. 1e-6
        uint24 fee;
        // whether the pool is locked
        bool unlocked;
    }
    /// @inheritdoc ISolidlyV3PoolState
    Slot0 public override slot0;

    // accumulated pool fees in token0/token1 units
    struct PoolFees {
        uint128 token0;
        uint128 token1;
    }
    /// @inheritdoc ISolidlyV3PoolState
    PoolFees public override poolFees;

    /// @inheritdoc ISolidlyV3PoolState
    uint128 public override liquidity;

    /// @inheritdoc ISolidlyV3PoolState
    mapping(int24 => Tick.Info) public override ticks;
    /// @inheritdoc ISolidlyV3PoolState
    mapping(int16 => uint256) public override tickBitmap;
    /// @inheritdoc ISolidlyV3PoolState
    mapping(bytes32 => Position.Info) public override positions;

    /// @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;
    }

    constructor() {
        int24 _tickSpacing;
        uint24 _fee;
        (factory, token0, token1, _fee, _tickSpacing) = ISolidlyV3PoolDeployer(msg.sender).parameters();
        slot0.fee = _fee;
        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 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 ISolidlyV3PoolActions
    /// @dev not locked because it initializes unlocked
    function initialize(uint160 sqrtPriceX96) external override {
        require(slot0.sqrtPriceX96 == 0, 'AI');

        int24 tick = TickMath.getTickAtSqrtRatio(sqrtPriceX96);

        slot0.sqrtPriceX96 = sqrtPriceX96;
        slot0.tick = tick;
        slot0.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 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);

        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

                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
    function _updatePosition(
        address owner,
        int24 tickLower,
        int24 tickUpper,
        int128 liquidityDelta
    ) private returns (Position.Info storage position) {
        position = positions.get(owner, tickLower, tickUpper);

        // if we need to update the ticks, do it
        bool flippedLower;
        bool flippedUpper;
        if (liquidityDelta != 0) {
            flippedLower = ticks.update(tickLower, liquidityDelta, false, maxLiquidityPerTick);
            flippedUpper = ticks.update(tickUpper, liquidityDelta, true, maxLiquidityPerTick);

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

        position.update(liquidityDelta);

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

    /// @inheritdoc ISolidlyV3PoolActions
    function mint(
        address recipient,
        int24 tickLower,
        int24 tickUpper,
        uint128 amount
    ) external override returns (uint256 amount0, uint256 amount1) {
        (amount0, amount1) = _mint(recipient, tickLower, tickUpper, amount);
    }

    /// @inheritdoc ISolidlyV3PoolActions
    function mint(
        address recipient,
        int24 tickLower,
        int24 tickUpper,
        uint128 amount,
        bytes calldata data
    ) external override returns (uint256 amount0, uint256 amount1) {
        (amount0, amount1) = _mint(recipient, tickLower, tickUpper, amount, data);
    }

    /// @inheritdoc ISolidlyV3PoolActions
    function mint(
        address recipient,
        int24 tickLower,
        int24 tickUpper,
        uint128 amount,
        uint256 amount0Min,
        uint256 amount1Min,
        uint256 deadline
    ) external override checkDeadline(deadline) returns (uint256 amount0, uint256 amount1) {
        (amount0, amount1) = _mint(recipient, tickLower, tickUpper, amount);
        require(amount0 >= amount0Min && amount1 >= amount1Min, 'AL');
    }

    /// @inheritdoc ISolidlyV3PoolActions
    function mint(
        address recipient,
        int24 tickLower,
        int24 tickUpper,
        uint128 amount,
        uint256 amount0Min,
        uint256 amount1Min,
        uint256 deadline,
        bytes calldata data
    ) external override checkDeadline(deadline) returns (uint256 amount0, uint256 amount1) {
        (amount0, amount1) = _mint(recipient, tickLower, tickUpper, amount, data);
        require(amount0 >= amount0Min && amount1 >= amount1Min, 'AL');
    }

    function _mint(
        address recipient,
        int24 tickLower,
        int24 tickUpper,
        uint128 amount
    ) private 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);

        if (amount0 > 0) TransferHelper.safeTransferFrom(token0, msg.sender, address(this), amount0);
        if (amount1 > 0) TransferHelper.safeTransferFrom(token1, msg.sender, address(this), amount1);

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

    function _mint(
        address recipient,
        int24 tickLower,
        int24 tickUpper,
        uint128 amount,
        bytes calldata data
    ) private 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();
        ISolidlyV3MintCallback(msg.sender).solidlyV3MintCallback(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 ISolidlyV3PoolActions
    function burnAndCollect(
        address recipient,
        int24 tickLower,
        int24 tickUpper,
        uint128 amountToBurn,
        uint128 amount0ToCollect,
        uint128 amount1ToCollect
    )
        external
        override
        returns (uint256 amount0FromBurn, uint256 amount1FromBurn, uint128 amount0Collected, uint128 amount1Collected)
    {
        (amount0FromBurn, amount1FromBurn) = _burn(tickLower, tickUpper, amountToBurn);
        (amount0Collected, amount1Collected) = _collect(
            recipient,
            tickLower,
            tickUpper,
            amount0ToCollect,
            amount1ToCollect
        );
    }

    /// @inheritdoc ISolidlyV3PoolActions
    function burnAndCollect(
        address recipient,
        int24 tickLower,
        int24 tickUpper,
        uint128 amountToBurn,
        uint256 amount0FromBurnMin,
        uint256 amount1FromBurnMin,
        uint128 amount0ToCollect,
        uint128 amount1ToCollect,
        uint256 deadline
    )
        external
        override
        checkDeadline(deadline)
        returns (uint256 amount0FromBurn, uint256 amount1FromBurn, uint128 amount0Collected, uint128 amount1Collected)
    {
        (amount0FromBurn, amount1FromBurn) = _burn(tickLower, tickUpper, amountToBurn);
        require(amount0FromBurn >= amount0FromBurnMin && amount1FromBurn >= amount1FromBurnMin, 'AL');
        (amount0Collected, amount1Collected) = _collect(
            recipient,
            tickLower,
            tickUpper,
            amount0ToCollect,
            amount1ToCollect
        );
    }

    /// @inheritdoc ISolidlyV3PoolActions
    function collect(
        address recipient,
        int24 tickLower,
        int24 tickUpper,
        uint128 amount0Requested,
        uint128 amount1Requested
    ) external override returns (uint128 amount0, uint128 amount1) {
        (amount0, amount1) = _collect(recipient, tickLower, tickUpper, amount0Requested, amount1Requested);
    }

    function _collect(
        address recipient,
        int24 tickLower,
        int24 tickUpper,
        uint128 amount0Requested,
        uint128 amount1Requested
    ) private 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 ISolidlyV3PoolActions
    function burn(
        int24 tickLower,
        int24 tickUpper,
        uint128 amount
    ) external override returns (uint256 amount0, uint256 amount1) {
        (amount0, amount1) = _burn(tickLower, tickUpper, amount);
    }

    /// @inheritdoc ISolidlyV3PoolActions
    function burn(
        int24 tickLower,
        int24 tickUpper,
        uint128 amount,
        uint256 amount0Min,
        uint256 amount1Min,
        uint256 deadline
    ) external override checkDeadline(deadline) returns (uint256 amount0, uint256 amount1) {
        (amount0, amount1) = _burn(tickLower, tickUpper, amount);
        require(amount0 >= amount0Min && amount1 >= amount1Min, 'AL');
    }

    function _burn(
        int24 tickLower,
        int24 tickUpper,
        uint128 amount
    ) private 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);
    }

    // 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 current liquidity in range
        uint128 liquidity;
        // the pool fee
        uint128 poolFee;
    }

    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 ISolidlyV3PoolActions
    function swap(
        address recipient,
        bool zeroForOne,
        int256 amountSpecified,
        uint160 sqrtPriceLimitX96
    ) external override returns (int256 amount0, int256 amount1) {
        (amount0, amount1) = _swap(recipient, zeroForOne, amountSpecified, sqrtPriceLimitX96);
    }

    /// @inheritdoc ISolidlyV3PoolActions
    function swap(
        address recipient,
        bool zeroForOne,
        int256 amountSpecified,
        uint160 sqrtPriceLimitX96,
        bytes calldata data
    ) external override returns (int256 amount0, int256 amount1) {
        (amount0, amount1) = _swap(recipient, zeroForOne, amountSpecified, sqrtPriceLimitX96, data);
    }

    /// @inheritdoc ISolidlyV3PoolActions
    function swap(
        address recipient,
        bool zeroForOne,
        int256 amountSpecified,
        uint160 sqrtPriceLimitX96,
        uint256 amountLimit,
        uint256 deadline
    ) external override checkDeadline(deadline) returns (int256 amount0, int256 amount1) {
        (amount0, amount1) = _swap(recipient, zeroForOne, amountSpecified, sqrtPriceLimitX96);
        if (zeroForOne) {
            require(uint256(-amount1) >= amountLimit, 'AL');
        } else {
            require(uint256(-amount0) >= amountLimit, 'AL');
        }
    }

    /// @inheritdoc ISolidlyV3PoolActions
    function swap(
        address recipient,
        bool zeroForOne,
        int256 amountSpecified,
        uint160 sqrtPriceLimitX96,
        uint256 amountLimit,
        uint256 deadline,
        bytes calldata data
    ) external override checkDeadline(deadline) returns (int256 amount0, int256 amount1) {
        (amount0, amount1) = _swap(recipient, zeroForOne, amountSpecified, sqrtPriceLimitX96, data);
        if (zeroForOne) {
            require(uint256(-amount1) >= amountLimit, 'AL');
        } else {
            require(uint256(-amount0) >= amountLimit, 'AL');
        }
    }

    /// @inheritdoc ISolidlyV3PoolActions
    function swap(
        address recipient,
        bool zeroForOne,
        int256 amountSpecified,
        uint160 sqrtPriceLimitX96,
        uint256 trackingCode
    ) external override returns (int256 amount0, int256 amount1) {
        (amount0, amount1) = _swap(recipient, zeroForOne, amountSpecified, sqrtPriceLimitX96);
    }

    /// @inheritdoc ISolidlyV3PoolActions
    function swap(
        address recipient,
        bool zeroForOne,
        int256 amountSpecified,
        uint160 sqrtPriceLimitX96,
        bytes calldata data,
        uint256 trackingCode
    ) external override returns (int256 amount0, int256 amount1) {
        (amount0, amount1) = _swap(recipient, zeroForOne, amountSpecified, sqrtPriceLimitX96, data);
    }

    /// @inheritdoc ISolidlyV3PoolActions
    function swap(
        address recipient,
        bool zeroForOne,
        int256 amountSpecified,
        uint160 sqrtPriceLimitX96,
        uint256 amountLimit,
        uint256 deadline,
        uint256 trackingCode
    ) external override checkDeadline(deadline) returns (int256 amount0, int256 amount1) {
        (amount0, amount1) = _swap(recipient, zeroForOne, amountSpecified, sqrtPriceLimitX96);
        if (zeroForOne) {
            require(uint256(-amount1) >= amountLimit, 'AL');
        } else {
            require(uint256(-amount0) >= amountLimit, 'AL');
        }
    }

    /// @inheritdoc ISolidlyV3PoolActions
    function swap(
        address recipient,
        bool zeroForOne,
        int256 amountSpecified,
        uint160 sqrtPriceLimitX96,
        uint256 amountLimit,
        uint256 deadline,
        bytes calldata data,
        uint256 trackingCode
    ) external override checkDeadline(deadline) returns (int256 amount0, int256 amount1) {
        (amount0, amount1) = _swap(recipient, zeroForOne, amountSpecified, sqrtPriceLimitX96, data);
        if (zeroForOne) {
            require(uint256(-amount1) >= amountLimit, 'AL');
        } else {
            require(uint256(-amount0) >= amountLimit, 'AL');
        }
    }

    function _swap(
        address recipient,
        bool zeroForOne,
        int256 amountSpecified,
        uint160 sqrtPriceLimitX96
    ) private returns (int256 amount0, int256 amount1) {
        (amount0, amount1) = _swapBase(recipient, zeroForOne, amountSpecified, sqrtPriceLimitX96);

        // do the transfers and collect payment
        if (zeroForOne) {
            if (amount0 > 0) TransferHelper.safeTransferFrom(token0, msg.sender, address(this), uint256(amount0));
            if (amount1 < 0) TransferHelper.safeTransfer(token1, recipient, uint256(-amount1));
        } else {
            if (amount1 > 0) TransferHelper.safeTransferFrom(token1, msg.sender, address(this), uint256(amount1));
            if (amount0 < 0) TransferHelper.safeTransfer(token0, recipient, uint256(-amount0));
        }

        slot0.unlocked = true;
    }

    function _swap(
        address recipient,
        bool zeroForOne,
        int256 amountSpecified,
        uint160 sqrtPriceLimitX96,
        bytes calldata data
    ) private returns (int256 amount0, int256 amount1) {
        (amount0, amount1) = _swapBase(recipient, zeroForOne, amountSpecified, sqrtPriceLimitX96);

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

            uint256 balance0Before = balance0();
            ISolidlyV3SwapCallback(msg.sender).solidlyV3SwapCallback(amount0, amount1, data);
            require(balance0Before.add(uint256(amount0)) <= balance0(), 'IIA');
        } else {
            if (amount0 < 0) TransferHelper.safeTransfer(token0, recipient, uint256(-amount0));

            uint256 balance1Before = balance1();
            ISolidlyV3SwapCallback(msg.sender).solidlyV3SwapCallback(amount0, amount1, data);
            require(balance1Before.add(uint256(amount1)) <= balance1(), 'IIA');
        }

        slot0.unlocked = true;
    }

    function _swapBase(
        address recipient,
        bool zeroForOne,
        int256 amountSpecified,
        uint160 sqrtPriceLimitX96
    ) private 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;

        uint128 liquidityStart = liquidity;

        bool exactInput = amountSpecified > 0;

        SwapState memory state = SwapState({
            amountSpecifiedRemaining: amountSpecified,
            amountCalculated: 0,
            sqrtPriceX96: slot0Start.sqrtPriceX96,
            tick: slot0Start.tick,
            liquidity: liquidityStart,
            poolFee: 0
        });

        // 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,
                slot0Start.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());
            }

            // increment poolFees for the current swap step
            state.poolFee += uint128(step.feeAmount);

            // 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) {
                    int128 liquidityNet = ticks.cross(step.tickNext);
                    // 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 if the tick changed
        if (state.tick != slot0Start.tick) {
            (slot0.sqrtPriceX96, slot0.tick) = (state.sqrtPriceX96, state.tick);
        } else {
            // otherwise just update the price
            slot0.sqrtPriceX96 = state.sqrtPriceX96;
        }

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

        // update pool fees
        // overflow is acceptable, fees must be claimed and reset before they hit type(uint128).max
        if (zeroForOne) {
            if (state.poolFee > 0) poolFees.token0 += state.poolFee;
        } else {
            if (state.poolFee > 0) poolFees.token1 += state.poolFee;
        }

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

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

    function quoteSwap(
        bool zeroForOne,
        int256 amountSpecified,
        uint160 sqrtPriceLimitX96
    )
        external
        view
        override
        returns (int256 amount0, int256 amount1, uint160 sqrtPriceX96After, int24 tickAfter, uint128 liquidityAfter)
    {
        require(amountSpecified != 0, 'AS');

        Slot0 memory slot0Start = slot0;

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

        uint128 liquidityStart = liquidity;

        bool exactInput = amountSpecified > 0;

        SwapState memory state = SwapState({
            amountSpecifiedRemaining: amountSpecified,
            amountCalculated: 0,
            sqrtPriceX96: slot0Start.sqrtPriceX96,
            tick: slot0Start.tick,
            liquidity: liquidityStart,
            poolFee: 0
        });

        // 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,
                slot0Start.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());
            }

            // increment poolFees for the current swap step
            state.poolFee += uint128(step.feeAmount);

            // 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) {
                    int128 liquidityNet = ticks.cross(step.tickNext);
                    // 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);
            }
        }

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

        return (amount0, amount1, state.sqrtPriceX96, state.tick, state.liquidity);
    }

    /// @inheritdoc ISolidlyV3PoolActions
    function flash(address recipient, uint256 amount0, uint256 amount1, bytes calldata data) external override lock {
        uint128 _liquidity = liquidity;
        require(_liquidity > 0, 'L');

        uint256 fee0 = FullMath.mulDivRoundingUp(amount0, slot0.fee, 1e6);
        uint256 fee1 = FullMath.mulDivRoundingUp(amount1, slot0.fee, 1e6);
        uint256 balance0Before = balance0();
        uint256 balance1Before = balance1();

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

        ISolidlyV3FlashCallback(msg.sender).solidlyV3FlashCallback(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) {
            poolFees.token0 += uint128(paid0);
        }
        if (paid1 > 0) {
            poolFees.token1 += uint128(paid1);
        }

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

    /// @inheritdoc ISolidlyV3PoolOwnerActions
    function setFee(uint24 fee) external override lock {
        require(ISolidlyV3Factory(factory).isFeeSetter(msg.sender) == 1, 'UA');
        // pool fee capped at 10%
        require(fee <= 100000);
        uint24 feeOld = slot0.fee;
        slot0.fee = fee;
        emit SetFee(feeOld, fee);
    }

    /// @inheritdoc ISolidlyV3PoolOwnerActions
    function collectProtocol(
        address recipient,
        uint128 amount0Requested,
        uint128 amount1Requested
    ) external override lock returns (uint128 amount0, uint128 amount1) {
        require(ISolidlyV3Factory(factory).feeCollector() == msg.sender, 'UA');

        amount0 = amount0Requested > poolFees.token0 ? poolFees.token0 : amount0Requested;
        amount1 = amount1Requested > poolFees.token1 ? poolFees.token1 : amount1Requested;

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

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