// File: contracts/ConvergentCurvePool.sol



// SPDX-License-Identifier: Apache-2.0
pragma solidity ^0.7.0;
pragma experimental ABIEncoderV2;

import "./interfaces/IERC20Decimals.sol";
import "./balancer-core-v2/lib/math/LogExpMath.sol";
import "./balancer-core-v2/lib/math/FixedPoint.sol";
import "./balancer-core-v2/vault/interfaces/IMinimalSwapInfoPool.sol";
import "./balancer-core-v2/vault/interfaces/IVault.sol";
import "./balancer-core-v2/pools/BalancerPoolToken.sol";

contract ConvergentCurvePool is IMinimalSwapInfoPool, BalancerPoolToken {
    using LogExpMath for uint256;
    using FixedPoint for uint256;

    // The token we expect to stay constant in value
    IERC20 public immutable underlying;
    uint8 public immutable underlyingDecimals;
    // The token we expect to appreciate to match underlying
    IERC20 public immutable bond;
    uint8 public immutable bondDecimals;
    // The expiration time
    uint256 public immutable expiration;
    // The number of seconds in our timescale
    uint256 public immutable unitSeconds;
    // The Balancer pool data
    // Note we change style to match Balancer's custom getter
    IVault private immutable _vault;
    bytes32 private immutable _poolId;

    // The fees recorded during swaps. These will be 18 point not token decimal encoded
    uint128 public feesUnderlying;
    uint128 public feesBond;
    // Stored records of governance tokens
    address public immutable governance;
    // The percent of each trade's implied yield to collect as LP fee
    uint256 public immutable percentFee;
    // The percent of LP fees that is payed to governance
    uint256 public immutable percentFeeGov;

    // Store constant token indexes for ascending sorted order
    // In this case despite these being internal it's cleaner
    // to ignore linting rules that require _
    /* solhint-disable private-vars-leading-underscore */
    uint256 internal immutable baseIndex;
    uint256 internal immutable bondIndex;
    /* solhint-enable private-vars-leading-underscore */

    // The max percent fee for governance, immutable after compilation
    uint256 public constant FEE_BOUND = 3e17;

    /// @notice This event allows the frontend to track the fees
    /// @param collectedBase the base asset tokens fees collected in this txn
    /// @param collectedBond the bond asset tokens fees collected in this txn
    /// @param remainingBase the amount of base asset fees have been charged but not collected
    /// @param remainingBond the amount of bond asset fees have been charged but not collected
    /// @dev All values emitted by this event are 18 point fixed not token native decimals
    event FeeCollection(
        uint256 collectedBase,
        uint256 collectedBond,
        uint256 remainingBase,
        uint256 remainingBond
    );

    /// @dev We need need to set the immutables on contract creation
    ///      Note - We expect both 'bond' and 'underlying' to have 'decimals()'
    /// @param _underlying The asset which the second asset should appreciate to match
    /// @param _bond The asset which should be appreciating
    /// @param _expiration The time in unix seconds when the bond asset should equal the underlying asset
    /// @param _unitSeconds The number of seconds in a unit of time, for example 1 year in seconds
    /// @param vault The balancer vault
    /// @param _percentFee The percent each trade's yield to collect as fees
    /// @param _percentFeeGov The percent of collected that go to governance
    /// @param _governance The address which gets minted reward lp
    /// @param name The balancer pool token name
    /// @param symbol The balancer pool token symbol
    constructor(
        IERC20 _underlying,
        IERC20 _bond,
        uint256 _expiration,
        uint256 _unitSeconds,
        IVault vault,
        uint256 _percentFee,
        uint256 _percentFeeGov,
        address _governance,
        string memory name,
        string memory symbol
    ) BalancerPoolToken(name, symbol) {
        // Sanity Check
        require(_expiration - block.timestamp < _unitSeconds);
        // Initialization on the vault
        bytes32 poolId = vault.registerPool(
            IVault.PoolSpecialization.TWO_TOKEN
        );

        IERC20[] memory tokens = new IERC20[](2);
        if (_underlying < _bond) {
            tokens[0] = _underlying;
            tokens[1] = _bond;
        } else {
            tokens[0] = _bond;
            tokens[1] = _underlying;
        }

        // Pass in zero addresses for Asset Managers
        // Note - functions below assume this token order
        vault.registerTokens(poolId, tokens, new address[](2));

        // Set immutable state variables
        _vault = vault;
        _poolId = poolId;
        percentFee = _percentFee;
        // We check that the gov percent fee is less than bound
        require(_percentFeeGov < FEE_BOUND, "Fee too high");
        percentFeeGov = _percentFeeGov;
        underlying = _underlying;
        underlyingDecimals = IERC20Decimals(address(_underlying)).decimals();
        bond = _bond;
        bondDecimals = IERC20Decimals(address(_bond)).decimals();
        expiration = _expiration;
        unitSeconds = _unitSeconds;
        governance = _governance;
        // Calculate the preset indexes for ordering
        bool underlyingFirst = _underlying < _bond;
        baseIndex = underlyingFirst ? 0 : 1;
        bondIndex = underlyingFirst ? 1 : 0;
    }

    // Balancer Interface required Getters

    /// @dev Returns the vault for this pool
    /// @return The vault for this pool
    function getVault() external view returns (IVault) {
        return _vault;
    }

    /// @dev Returns the poolId for this pool
    /// @return The poolId for this pool
    function getPoolId() external view returns (bytes32) {
        return _poolId;
    }

    // Trade Functionality

    /// @dev Called by the Vault on swaps to get a price quote
    /// @param swapRequest The request which contains the details of the swap
    /// @param currentBalanceTokenIn The input token balance
    /// @param currentBalanceTokenOut The output token balance
    /// @return the amount of the output or input token amount of for swap
    function onSwap(
        SwapRequest memory swapRequest,
        uint256 currentBalanceTokenIn,
        uint256 currentBalanceTokenOut
    ) public override returns (uint256) {
        // Check that the sender is pool, we change state so must make
        // this check.
        require(msg.sender == address(_vault), "Non Vault caller");
        // Tokens amounts are passed to us in decimal form of the tokens
        // But we want theme in 18 point
        uint256 amount;
        bool isOutputSwap = swapRequest.kind == IVault.SwapKind.GIVEN_IN;
        if (isOutputSwap) {
            amount = _tokenToFixed(swapRequest.amount, swapRequest.tokenIn);
        } else {
            amount = _tokenToFixed(swapRequest.amount, swapRequest.tokenOut);
        }
        currentBalanceTokenIn = _tokenToFixed(
            currentBalanceTokenIn,
            swapRequest.tokenIn
        );
        currentBalanceTokenOut = _tokenToFixed(
            currentBalanceTokenOut,
            swapRequest.tokenOut
        );

        // We apply the trick which is used in the paper and
        // double count the reserves because the curve provisions liquidity
        // for prices above one underlying per bond, which we don't want to be accessible
        (uint256 tokenInReserve, uint256 tokenOutReserve) = _adjustedReserve(
            currentBalanceTokenIn,
            swapRequest.tokenIn,
            currentBalanceTokenOut,
            swapRequest.tokenOut
        );

        // We switch on if this is an input or output case
        if (isOutputSwap) {
            // We get quote
            uint256 quote = solveTradeInvariant(
                amount,
                tokenInReserve,
                tokenOutReserve,
                isOutputSwap
            );
            // We assign the trade fee
            quote = _assignTradeFee(amount, quote, swapRequest.tokenOut, false);
            // We return the quote
            return _fixedToToken(quote, swapRequest.tokenOut);
        } else {
            // We get the quote
            uint256 quote = solveTradeInvariant(
                amount,
                tokenOutReserve,
                tokenInReserve,
                isOutputSwap
            );
            // We assign the trade fee
            quote = _assignTradeFee(quote, amount, swapRequest.tokenOut, true);
            // We return the output
            return _fixedToToken(quote, swapRequest.tokenIn);
        }
    }

    /// @dev Hook for joining the pool that must be called from the vault.
    ///      It mints a proportional number of tokens compared to current LP pool,
    ///      based on the maximum input the user indicates.
    /// @param poolId The balancer pool id, checked to ensure non erroneous vault call
    // @param sender Unused by this pool but in interface
    /// @param recipient The address which will receive lp tokens.
    /// @param currentBalances The current pool balances, sorted by address low to high.  length 2
    // @param latestBlockNumberUsed last block number unused in this pool
    /// @param protocolSwapFee The percent of pool fees to be paid to the Balancer Protocol
    /// @param userData Abi encoded fixed length 2 array containing max inputs also sorted by
    ///                 address low to high
    /// @return amountsIn The actual amounts of token the vault should move to this pool
    /// @return dueProtocolFeeAmounts The amounts of each token to pay as protocol fees
    function onJoinPool(
        bytes32 poolId,
        address, // sender
        address recipient,
        uint256[] memory currentBalances,
        uint256,
        uint256 protocolSwapFee,
        bytes calldata userData
    )
        external
        override
        returns (
            uint256[] memory amountsIn,
            uint256[] memory dueProtocolFeeAmounts
        )
    {
        // Default checks
        require(msg.sender == address(_vault), "Non Vault caller");
        require(poolId == _poolId, "Wrong pool id");
        uint256[] memory maxAmountsIn = abi.decode(userData, (uint256[]));
        require(
            currentBalances.length == 2 && maxAmountsIn.length == 2,
            "Invalid format"
        );
        // We must normalize the inputs to 18 point
        _normalizeSortedArray(currentBalances);
        _normalizeSortedArray(maxAmountsIn);

        // Mint LP to the governance address.
        // The {} zoning here helps solidity figure out the stack
        {
            (
                uint256 localFeeUnderlying,
                uint256 localFeeBond
            ) = _mintGovernanceLP(currentBalances);
            dueProtocolFeeAmounts = new uint256[](2);

            dueProtocolFeeAmounts[baseIndex] = localFeeUnderlying.mulDown(
                protocolSwapFee
            );
            dueProtocolFeeAmounts[bondIndex] = localFeeBond.mulDown(
                protocolSwapFee
            );
        }
        // Mint for the user
        amountsIn = _mintLP(
            maxAmountsIn[baseIndex],
            maxAmountsIn[bondIndex],
            currentBalances,
            recipient
        );

        // We now have make the outputs have the correct decimals
        _denormalizeSortedArray(amountsIn);
        _denormalizeSortedArray(dueProtocolFeeAmounts);
    }

    /// @dev Hook for leaving the pool that must be called from the vault.
    ///      It burns a proportional number of tokens compared to current LP pool,
    ///      based on the minium output the user wants.
    /// @param poolId The balancer pool id, checked to ensure non erroneous vault call
    // @param sender Unused by this pool but in interface
    /// @param recipient The address which will receive the withdraw tokens.
    /// @param currentBalances The current pool balances, sorted by address low to high.  length 2
    // @param latestBlockNumberUsed last block number unused in this pool
    /// @param protocolSwapFee The percent of pool fees to be paid to the Balancer Protocol
    /// @param userData Abi encoded fixed length 2 array containing min outputs also sorted by
    ///                 address low to high
    /// @return amountsOut The number of each token to send to the caller
    /// @return dueProtocolFeeAmounts The amounts of each token to pay as protocol fees
    function onExitPool(
        bytes32 poolId,
        address,
        address recipient,
        uint256[] memory currentBalances,
        uint256,
        uint256 protocolSwapFee,
        bytes calldata userData
    )
        external
        override
        returns (
            uint256[] memory amountsOut,
            uint256[] memory dueProtocolFeeAmounts
        )
    {
        // Default checks
        require(msg.sender == address(_vault), "Non Vault caller");
        require(poolId == _poolId, "Wrong pool id");
        uint256[] memory minAmountsOut = abi.decode(userData, (uint256[]));
        require(
            currentBalances.length == 2 && minAmountsOut.length == 2,
            "Invalid format"
        );
        // We have to convert to 18 decimals
        _normalizeSortedArray(currentBalances);
        _normalizeSortedArray(minAmountsOut);

        // Mint LP for the governance address.
        // {} zones to help solidity figure out the stack
        {
            (
                uint256 localFeeUnderlying,
                uint256 localFeeBond
            ) = _mintGovernanceLP(currentBalances);

            // Calculate the amount of fees for balancer to collect
            dueProtocolFeeAmounts = new uint256[](2);
            dueProtocolFeeAmounts[baseIndex] = localFeeUnderlying.mulDown(
                protocolSwapFee
            );
            dueProtocolFeeAmounts[bondIndex] = localFeeBond.mulDown(
                protocolSwapFee
            );
        }

        amountsOut = _burnLP(
            minAmountsOut[baseIndex],
            minAmountsOut[bondIndex],
            currentBalances,
            recipient
        );

        // We need to convert the balancer outputs to token decimals instead of 18
        _denormalizeSortedArray(amountsOut);
        _denormalizeSortedArray(dueProtocolFeeAmounts);
        return (amountsOut, dueProtocolFeeAmounts);
    }

    /// @dev Returns the balances so that they'll be in the order [underlying, bond].
    /// @param currentBalances balances sorted low to high of address value.
    function _getSortedBalances(uint256[] memory currentBalances)
        internal
        view
        returns (uint256 underlyingBalance, uint256 bondBalance)
    {
        return (currentBalances[baseIndex], currentBalances[bondIndex]);
    }

    /// @dev Turns an array of token amounts into an array of 18 point amounts
    /// @param data The data to normalize
    function _normalizeSortedArray(uint256[] memory data) internal view {
        data[baseIndex] = _normalize(data[baseIndex], underlyingDecimals, 18);
        data[bondIndex] = _normalize(data[bondIndex], bondDecimals, 18);
    }

    /// @dev Turns an array of 18 point amounts into token amounts
    /// @param data The data to turn in to token decimals
    function _denormalizeSortedArray(uint256[] memory data) internal view {
        data[baseIndex] = _normalize(data[baseIndex], 18, underlyingDecimals);
        data[bondIndex] = _normalize(data[bondIndex], 18, bondDecimals);
    }

    // Math libraries and internal routing

    /// @dev Calculates how many tokens should be outputted given an input plus reserve variables
    ///      Assumes all inputs are in 18 point fixed compatible with the balancer fixed math lib.
    ///      Since solving for an input is almost exactly the same as an output you can indicate
    ///      if this is an input or output calculation in the call.
    /// @param amountX The amount of token x sent in normalized to have 18 decimals
    /// @param reserveX The amount of the token x currently held by the pool normalized to 18 decimals
    /// @param reserveY The amount of the token y currently held by the pool normalized to 18 decimals
    /// @param out Is true if the pool will receive amountX and false if it is expected to produce it.
    /// @return Either if 'out' is true the amount of Y token to send to the user or
    ///         if 'out' is false the amount of Y Token to take from the user
    function solveTradeInvariant(
        uint256 amountX,
        uint256 reserveX,
        uint256 reserveY,
        bool out
    ) public view returns (uint256) {
        // Gets 1 - t
        uint256 a = _getYieldExponent();
        // calculate x before ^ a
        uint256 xBeforePowA = LogExpMath.pow(reserveX, a);
        // calculate y before ^ a
        uint256 yBeforePowA = LogExpMath.pow(reserveY, a);
        // calculate x after ^ a
        uint256 xAfterPowA = out
            ? LogExpMath.pow(reserveX + amountX, a)
            : LogExpMath.pow(reserveX.sub(amountX), a);
        // Calculate y_after = ( x_before ^a + y_ before ^a -  x_after^a)^(1/a)
        // Will revert with underflow here if the liquidity isn't enough for the trade
        uint256 yAfter = (xBeforePowA + yBeforePowA).sub(xAfterPowA);
        // Note that this call is to FixedPoint Div so works as intended
        yAfter = LogExpMath.pow(yAfter, uint256(FixedPoint.ONE).divDown(a));
        // The amount of Y token to send is (reserveY_before - reserveY_after)
        return out ? reserveY.sub(yAfter) : yAfter.sub(reserveY);
    }

    /// @dev Adds a fee equal to to 'feePercent' of remaining interest to each trade
    ///      This function accepts both input and output trades, amd expects that all
    ///      inputs are in fixed 18 point
    /// @param amountIn The trade's amountIn in fixed 18 point
    /// @param amountOut The trade's amountOut in fixed 18 point
    /// @param outputToken The output token
    /// @param isInputTrade True if the trader is requesting a quote for the amount of input
    ///                     they need to provide to get 'amountOut' false otherwise
    /// @return The updated output quote
    //  Note - The safe math in this function implicitly prevents the price of 'bond' in underlying
    //         from being higher than 1.
    function _assignTradeFee(
        uint256 amountIn,
        uint256 amountOut,
        IERC20 outputToken,
        bool isInputTrade
    ) internal returns (uint256) {
        // The math splits on if this is input or output
        if (isInputTrade) {
            // Then it splits again on which token is the bond
            if (outputToken == bond) {
                // If the output is bond the implied yield is out - in
                uint256 impliedYieldFee = percentFee.mulDown(
                    amountOut.sub(amountIn)
                );
                // we record that fee collected from the underlying
                feesUnderlying += uint128(impliedYieldFee);
                // and return the adjusted input quote
                return amountIn.add(impliedYieldFee);
            } else {
                // If the input token is bond the implied yield is in - out
                uint256 impliedYieldFee = percentFee.mulDown(
                    amountIn.sub(amountOut)
                );
                // we record that collected fee from the input bond
                feesBond += uint128(impliedYieldFee);
                // and return the updated input quote
                return amountIn.add(impliedYieldFee);
            }
        } else {
            if (outputToken == bond) {
                // If the output is bond the implied yield is out - in
                uint256 impliedYieldFee = percentFee.mulDown(
                    amountOut.sub(amountIn)
                );
                // we record that fee collected from the bond output
                feesBond += uint128(impliedYieldFee);
                // and then return the updated output
                return amountOut.sub(impliedYieldFee);
            } else {
                // If the output is underlying the implied yield is in - out
                uint256 impliedYieldFee = percentFee.mulDown(
                    amountIn.sub(amountOut)
                );
                // we record the collected underlying fee
                feesUnderlying += uint128(impliedYieldFee);
                // and then return the updated output quote
                return amountOut.sub(impliedYieldFee);
            }
        }
    }

    /// @dev Mints the maximum possible LP given a set of max inputs
    /// @param inputUnderlying The max underlying to deposit
    /// @param inputBond The max bond to deposit
    /// @param currentBalances The current pool balances, sorted by address low to high.  length 2
    /// @param recipient The person who receives the lp funds
    /// @return amountsIn The actual amounts of token deposited in token sorted order
    function _mintLP(
        uint256 inputUnderlying,
        uint256 inputBond,
        uint256[] memory currentBalances,
        address recipient
    ) internal returns (uint256[] memory amountsIn) {
        // Initialize the memory array with length
        amountsIn = new uint256[](2);
        // Passing in in memory array helps stack but we use locals for better names
        (uint256 reserveUnderlying, uint256 reserveBond) = _getSortedBalances(
            currentBalances
        );

        uint256 localTotalSupply = totalSupply();
        // Check if the pool is initialized
        if (localTotalSupply == 0) {
            // When uninitialized we mint exactly the underlying input
            // in LP tokens
            _mintPoolTokens(recipient, inputUnderlying);
            // Return the right data
            amountsIn[baseIndex] = inputUnderlying;
            amountsIn[bondIndex] = 0;
            return (amountsIn);
        }
        // Get the reserve ratio, the say how many underlying per bond in the reserve
        // (input underlying / reserve underlying) is the percent increase caused by deposit
        uint256 underlyingPerBond = reserveUnderlying.divDown(reserveBond);
        // Use the underlying per bond to get the needed number of input underlying
        uint256 neededUnderlying = underlyingPerBond.mulDown(inputBond);

        // If the user can't provide enough underlying
        if (neededUnderlying > inputUnderlying) {
            // The increase in total supply is the input underlying
            // as a ratio to reserve
            uint256 mintAmount = (inputUnderlying.mulDown(localTotalSupply))
                .divDown(reserveUnderlying);
            // We mint a new amount of as the the percent increase given
            // by the ratio of the input underlying to the reserve underlying
            _mintPoolTokens(recipient, mintAmount);
            // In this case we use the whole input of underlying
            // and consume (inputUnderlying/underlyingPerBond) bonds
            amountsIn[baseIndex] = inputUnderlying;
            amountsIn[bondIndex] = inputUnderlying.divDown(underlyingPerBond);
        } else {
            // We calculate the percent increase in the reserves from contributing
            // all of the bond
            uint256 mintAmount = (neededUnderlying.mulDown(localTotalSupply))
                .divDown(reserveUnderlying);
            // We then mint an amount of pool token which corresponds to that increase
            _mintPoolTokens(recipient, mintAmount);
            // The indicate we consumed the input bond and (inputBond*underlyingPerBond)
            amountsIn[baseIndex] = neededUnderlying;
            amountsIn[bondIndex] = inputBond;
        }
    }

    /// @dev Burns at least enough LP tokens from the sender to produce
    ///      as set of minium outputs.
    /// @param minOutputUnderlying The minimum output in underlying
    /// @param minOutputBond The minimum output in the bond
    /// @param currentBalances The current pool balances, sorted by address low to high.  length 2
    /// @param source The address to burn from.
    /// @return amountsReleased in address sorted order
    function _burnLP(
        uint256 minOutputUnderlying,
        uint256 minOutputBond,
        uint256[] memory currentBalances,
        address source
    ) internal returns (uint256[] memory amountsReleased) {
        // Initialize the memory array with length
        amountsReleased = new uint256[](2);
        // We take in sorted token arrays to help the stack but
        // use local names to improve readability
        (uint256 reserveUnderlying, uint256 reserveBond) = _getSortedBalances(
            currentBalances
        );

        uint256 localTotalSupply = totalSupply();
        // Calculate the ratio of the minOutputUnderlying to reserve
        uint256 underlyingPerBond = reserveUnderlying.divDown(reserveBond);
        // If the ratio won't produce enough bond
        if (minOutputUnderlying > minOutputBond.mulDown(underlyingPerBond)) {
            // In this case we burn enough tokens to output 'minOutputUnderlying'
            // which will be the total supply times the percent of the underlying
            // reserve which this amount of underlying is.
            uint256 burned = (minOutputUnderlying.mulDown(localTotalSupply))
                .divDown(reserveUnderlying);
            _burnPoolTokens(source, burned);
            // We return that we released 'minOutputUnderlying' and the number of bonds that
            // preserves the reserve ratio
            amountsReleased[baseIndex] = minOutputUnderlying;
            amountsReleased[bondIndex] = minOutputUnderlying.divDown(
                underlyingPerBond
            );
        } else {
            // Then the amount burned is the ratio of the minOutputBond
            // to the reserve of bond times the total supply
            uint256 burned = (minOutputBond.mulDown(localTotalSupply)).divDown(
                reserveBond
            );
            _burnPoolTokens(source, burned);
            // We return that we released all of the minOutputBond
            // and the number of underlying which preserves the reserve ratio
            amountsReleased[baseIndex] = minOutputBond.mulDown(
                underlyingPerBond
            );
            amountsReleased[bondIndex] = minOutputBond;
        }
    }

    /// @dev Mints LP tokens from a percentage of the stored fees and then updates them
    /// @param currentBalances The current pool balances, sorted by address low to high.  length 2
    ///                        expects the inputs to be 18 point fixed
    /// @return Returns the fee amounts as (feeUnderlying, feeBond) to avoid other sloads
    function _mintGovernanceLP(uint256[] memory currentBalances)
        internal
        returns (uint256, uint256)
    {
        // Load and cast the stored fees
        // Note - Because of sizes should only be one sload
        uint256 localFeeUnderlying = uint256(feesUnderlying);
        uint256 localFeeBond = uint256(feesBond);
        if (percentFeeGov == 0) {
            // We reset this state because it is expected that this function
            // resets the amount to match what's consumed and in the zero fee case
            // that's everything.
            (feesUnderlying, feesBond) = (0, 0);
            // Emit a fee tracking event
            emit FeeCollection(localFeeUnderlying, localFeeBond, 0, 0);
            // Return the used fees
            return (localFeeUnderlying, localFeeBond);
        }

        // Calculate the gov fee which is the assigned fees times the
        // percent
        uint256 govFeeUnderlying = localFeeUnderlying.mulDown(percentFeeGov);
        uint256 govFeeBond = localFeeBond.mulDown(percentFeeGov);
        // Mint the actual LP for gov address
        uint256[] memory consumed = _mintLP(
            govFeeUnderlying,
            govFeeBond,
            currentBalances,
            governance
        );
        // We calculate the actual fees used
        uint256 usedFeeUnderlying = (consumed[baseIndex]).divDown(
            percentFeeGov
        );
        uint256 usedFeeBond = (consumed[bondIndex]).divDown(percentFeeGov);
        // Calculate the remaining fees, note due to rounding errors they are likely to
        // be true that usedFees + remainingFees > originalFees by a very small rounding error
        // this is safe as with a bounded gov fee it never consumes LP funds.
        uint256 remainingUnderlying = govFeeUnderlying
            .sub(consumed[baseIndex])
            .divDown(percentFeeGov);
        uint256 remainingBond = govFeeBond.sub(consumed[bondIndex]).divDown(
            percentFeeGov
        );
        // Emit fee tracking event
        emit FeeCollection(
            usedFeeUnderlying,
            usedFeeBond,
            remainingUnderlying,
            remainingBond
        );
        // Store the remaining fees
        feesUnderlying = uint128(remainingUnderlying);
        feesBond = uint128(remainingBond);
        // We return the fees which were removed from storage
        return (usedFeeUnderlying, usedFeeBond);
    }

    /// @dev Calculates 1 - t
    /// @return Returns 1 - t, encoded as a fraction in 18 decimal fixed point
    function _getYieldExponent() internal virtual view returns (uint256) {
        // The fractional time
        uint256 timeTillExpiry = block.timestamp < expiration
            ? expiration - block.timestamp
            : 0;
        timeTillExpiry *= 1e18;
        // timeTillExpiry now contains the a fixed point of the years remaining
        timeTillExpiry = timeTillExpiry.divDown(unitSeconds * 1e18);
        uint256 result = uint256(FixedPoint.ONE).sub(timeTillExpiry);
        // Sanity Check
        require(result != 0);
        // Return result
        return result;
    }

    /// @dev Applies the reserve adjustment from the paper and returns the reserves
    ///      Note: The inputs should be in 18 point fixed to match the LP decimals
    /// @param reserveTokenIn The reserve of the input token
    /// @param tokenIn The address of the input token
    /// @param reserveTokenOut The reserve of the output token
    /// @return Returns (adjustedReserveIn, adjustedReserveOut)
    function _adjustedReserve(
        uint256 reserveTokenIn,
        IERC20 tokenIn,
        uint256 reserveTokenOut,
        IERC20 tokenOut
    ) internal view returns (uint256, uint256) {
        // We need to identify the bond asset and the underlying
        // This check is slightly redundant in most cases but more secure
        if (tokenIn == underlying && tokenOut == bond) {
            // We return (underlyingReserve, bondReserve + totalLP)
            return (reserveTokenIn, reserveTokenOut + totalSupply());
        } else if (tokenIn == bond && tokenOut == underlying) {
            // We return (bondReserve + totalLP, underlyingReserve)
            return (reserveTokenIn + totalSupply(), reserveTokenOut);
        }
        // This should never be hit
        revert("Token request doesn't match stored");
    }

    /// @dev Turns a token which is either 'bond' or 'underlying' into 18 point decimal
    /// @param amount The amount of the token in native decimal encoding
    /// @param token The address of the token
    /// @return The amount of token encoded into 18 point fixed point
    function _tokenToFixed(uint256 amount, IERC20 token)
        internal
        view
        returns (uint256)
    {
        // In both cases we are targeting 18 point
        if (token == underlying) {
            return _normalize(amount, underlyingDecimals, 18);
        } else if (token == bond) {
            return _normalize(amount, bondDecimals, 18);
        }
        // Should never happen
        revert("Called with non pool token");
    }

    /// @dev Turns an 18 fixed point amount into a token amount
    ///       Token must be either 'bond' or 'underlying'
    /// @param amount The amount of the token in 18 decimal fixed point
    /// @param token The address of the token
    /// @return The amount of token encoded in native decimal point
    function _fixedToToken(uint256 amount, IERC20 token)
        internal
        view
        returns (uint256)
    {
        if (token == underlying) {
            // Recodes to 'underlyingDecimals' decimals
            return _normalize(amount, 18, underlyingDecimals);
        } else if (token == bond) {
            // Recodes to 'bondDecimals' decimals
            return _normalize(amount, 18, bondDecimals);
        }
        // Should never happen
        revert("Called with non pool token");
    }

    /// @dev Takes an 'amount' encoded with 'decimalsBefore' decimals and
    ///      re encodes it with 'decimalsAfter' decimals
    /// @param amount The amount to normalize
    /// @param decimalsBefore The decimal encoding before
    /// @param decimalsAfter The decimal encoding after
    function _normalize(
        uint256 amount,
        uint8 decimalsBefore,
        uint8 decimalsAfter
    ) internal pure returns (uint256) {
        // If we need to increase the decimals
        if (decimalsBefore > decimalsAfter) {
            // Then we shift right the amount by the number of decimals
            amount = amount / 10**(decimalsBefore - decimalsAfter);
            // If we need to decrease the number
        } else if (decimalsBefore < decimalsAfter) {
            // then we shift left by the difference
            amount = amount * 10**(decimalsAfter - decimalsBefore);
        }
        // If nothing changed this is a no-op
        return amount;
    }
}

// File: contracts/interfaces/IERC20Decimals.sol



// SPDX-License-Identifier: Apache-2.0
pragma solidity >=0.7.0;

import "../balancer-core-v2/lib/openzeppelin/ERC20.sol";

interface IERC20Decimals is IERC20 {
    // Non standard but almost all erc20 have this
    function decimals() external view returns (uint8);
}

// File: contracts/balancer-core-v2/lib/math/LogExpMath.sol



// SPDX-License-Identifier: MIT
// Permission is hereby granted, free of charge, to any person obtaining a copy of this software and associated
// documentation files (the “Software”), to deal in the Software without restriction, including without limitation the
// rights to use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of the Software, and to
// permit persons to whom the Software is furnished to do so, subject to the following conditions:

// The above copyright notice and this permission notice shall be included in all copies or substantial portions of the
// Software.

// THE SOFTWARE IS PROVIDED “AS IS”, WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE
// WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR
// COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR
// OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.

pragma solidity ^0.7.0;

import "../helpers/BalancerErrors.sol";

/* solhint-disable */

/**
 * @dev Exponentiation and logarithm functions for 18 decimal fixed point numbers (both base and exponent/argument).
 *
 * Exponentiation and logarithm with arbitrary bases (x^y and log_x(y)) are implemented by conversion to natural
 * exponentiation and logarithm (where the base is Euler's number).
 *
 * @author Fernando Martinelli - @fernandomartinelli
 * @author Sergio Yuhjtman - @sergioyuhjtman
 * @author Daniel Fernandez - @dmf7z
 */
library LogExpMath {
    // All fixed point multiplications and divisions are inlined. This means we need to divide by ONE when multiplying
    // two numbers, and multiply by ONE when dividing them.

    // All arguments and return values are 18 decimal fixed point numbers.
    int256 constant ONE_18 = 1e18;

    // Internally, intermediate values are computed with higher precision as 20 decimal fixed point numbers, and in the
    // case of ln36, 36 decimals.
    int256 constant ONE_20 = 1e20;
    int256 constant ONE_36 = 1e36;

    // The domain of natural exponentiation is bound by the word size and number of decimals used.
    //
    // Because internally the result will be stored using 20 decimals, the largest possible result is
    // (2^255 - 1) / 10^20, which makes the largest exponent ln((2^255 - 1) / 10^20) = 130.700829182905140221.
    // The smallest possible result is 10^(-18), which makes largest negative argument
    // ln(10^(-18)) = -41.446531673892822312.
    // We use 130.0 and -41.0 to have some safety margin.
    int256 constant MAX_NATURAL_EXPONENT = 130e18;
    int256 constant MIN_NATURAL_EXPONENT = -41e18;

    // Bounds for ln_36's argument. Both ln(0.9) and ln(1.1) can be represented with 36 decimal places in a fixed point
    // 256 bit integer.
    int256 constant LN_36_LOWER_BOUND = ONE_18 - 1e17;
    int256 constant LN_36_UPPER_BOUND = ONE_18 + 1e17;

    uint256 constant MILD_EXPONENT_BOUND = 2**254 / uint256(ONE_20);

    // 18 decimal constants
    int256 constant x0 = 128000000000000000000; // 2ˆ7
    int256 constant a0 = 38877084059945950922200000000000000000000000000000000000; // eˆ(x0) (no decimals)
    int256 constant x1 = 64000000000000000000; // 2ˆ6
    int256 constant a1 = 6235149080811616882910000000; // eˆ(x1) (no decimals)

    // 20 decimal constants
    int256 constant x2 = 3200000000000000000000; // 2ˆ5
    int256 constant a2 = 7896296018268069516100000000000000; // eˆ(x2)
    int256 constant x3 = 1600000000000000000000; // 2ˆ4
    int256 constant a3 = 888611052050787263676000000; // eˆ(x3)
    int256 constant x4 = 800000000000000000000; // 2ˆ3
    int256 constant a4 = 298095798704172827474000; // eˆ(x4)
    int256 constant x5 = 400000000000000000000; // 2ˆ2
    int256 constant a5 = 5459815003314423907810; // eˆ(x5)
    int256 constant x6 = 200000000000000000000; // 2ˆ1
    int256 constant a6 = 738905609893065022723; // eˆ(x6)
    int256 constant x7 = 100000000000000000000; // 2ˆ0
    int256 constant a7 = 271828182845904523536; // eˆ(x7)
    int256 constant x8 = 50000000000000000000; // 2ˆ-1
    int256 constant a8 = 164872127070012814685; // eˆ(x8)
    int256 constant x9 = 25000000000000000000; // 2ˆ-2
    int256 constant a9 = 128402541668774148407; // eˆ(x9)
    int256 constant x10 = 12500000000000000000; // 2ˆ-3
    int256 constant a10 = 113314845306682631683; // eˆ(x10)
    int256 constant x11 = 6250000000000000000; // 2ˆ-4
    int256 constant a11 = 106449445891785942956; // eˆ(x11)

    /**
     * @dev Exponentiation (x^y) with unsigned 18 decimal fixed point base and exponent.
     *
     * Reverts if ln(x) * y is smaller than `MIN_NATURAL_EXPONENT`, or larger than `MAX_NATURAL_EXPONENT`.
     */
    function pow(uint256 x, uint256 y) internal pure returns (uint256) {
        if (y == 0) {
            // We solve the 0^0 indetermination by making it equal one.
            return uint256(ONE_18);
        }

        if (x == 0) {
            return 0;
        }

        // Instead of computing x^y directly, we instead rely on the properties of logarithms and exponentiation to
        // arrive at that result. In particular, exp(ln(x)) = x, and ln(x^y) = y * ln(x). This means
        // x^y = exp(y * ln(x)).

        // The ln function takes a signed value, so we need to make sure x fits in the signed 256 bit range.
        _require(x < 2**255, Errors.X_OUT_OF_BOUNDS);
        int256 x_int256 = int256(x);

        // We will compute y * ln(x) in a single step. Depending on the value of x, we can either use ln or ln_36. In
        // both cases, we leave the division by ONE_18 (due to fixed point multiplication) to the end.

        // This prevents y * ln(x) from overflowing, and at the same time guarantees y fits in the signed 256 bit range.
        _require(y < MILD_EXPONENT_BOUND, Errors.Y_OUT_OF_BOUNDS);
        int256 y_int256 = int256(y);

        int256 logx_times_y;
        if (LN_36_LOWER_BOUND < x_int256 && x_int256 < LN_36_UPPER_BOUND) {
            int256 ln_36_x = _ln_36(x_int256);

            // ln_36_x has 36 decimal places, so multiplying by y_int256 isn't as straightforward, since we can't just
            // bring y_int256 to 36 decimal places, as it might overflow. Instead, we perform two 18 decimal
            // multiplications and add the results: one with the first 18 decimals of ln_36_x, and one with the
            // (downscaled) last 18 decimals.
            logx_times_y = ((ln_36_x / ONE_18) * y_int256 + ((ln_36_x % ONE_18) * y_int256) / ONE_18);
        } else {
            logx_times_y = _ln(x_int256) * y_int256;
        }
        logx_times_y /= ONE_18;

        // Finally, we compute exp(y * ln(x)) to arrive at x^y
        _require(
            MIN_NATURAL_EXPONENT <= logx_times_y && logx_times_y <= MAX_NATURAL_EXPONENT,
            Errors.PRODUCT_OUT_OF_BOUNDS
        );

        return uint256(exp(logx_times_y));
    }

    /**
     * @dev Natural exponentiation (e^x) with signed 18 decimal fixed point exponent.
     *
     * Reverts if `x` is smaller than MIN_NATURAL_EXPONENT, or larger than `MAX_NATURAL_EXPONENT`.
     */
    function exp(int256 x) internal pure returns (int256) {
        _require(x >= MIN_NATURAL_EXPONENT && x <= MAX_NATURAL_EXPONENT, Errors.INVALID_EXPONENT);

        if (x < 0) {
            // We only handle positive exponents: e^(-x) is computed as 1 / e^x. We can safely make x positive since it
            // fits in the signed 256 bit range (as it is larger than MIN_NATURAL_EXPONENT).
            // Fixed point division requires multiplying by ONE_18.
            return ((ONE_18 * ONE_18) / exp(-x));
        }

        // First, we use the fact that e^(x+y) = e^x * e^y to decompose x into a sum of powers of two, which we call x_n,
        // where x_n == 2^(7 - n), and e^x_n = a_n has been precomputed. We choose the first x_n, x0, to equal 2^7
        // because all larger powers are larger than MAX_NATURAL_EXPONENT, and therefore not present in the
        // decomposition.
        // At the end of this process we will have the product of all e^x_n = a_n that apply, and the remainder of this
        // decomposition, which will be lower than the smallest x_n.
        // exp(x) = k_0 * a_0 * k_1 * a_1 * ... + k_n * a_n * exp(remainder), where each k_n equals either 0 or 1.
        // We mutate x by subtracting x_n, making it the remainder of the decomposition.

        // The first two a_n (e^(2^7) and e^(2^6)) are too large if stored as 18 decimal numbers, and could cause
        // intermediate overflows. Instead we store them as plain integers, with 0 decimals.
        // Additionally, x0 + x1 is larger than MAX_NATURAL_EXPONENT, which means they will not both be present in the
        // decomposition.

        // For each x_n, we test if that term is present in the decomposition (if x is larger than it), and if so deduct
        // it and compute the accumulated product.

        int256 firstAN;
        if (x >= x0) {
            x -= x0;
            firstAN = a0;
        } else if (x >= x1) {
            x -= x1;
            firstAN = a1;
        } else {
            firstAN = 1; // One with no decimal places
        }

        // We now transform x into a 20 decimal fixed point number, to have enhanced precision when computing the
        // smaller terms.
        x *= 100;

        // `product` is the accumulated product of all a_n (except a0 and a1), which starts at 20 decimal fixed point
        // one. Recall that fixed point multiplication requires dividing by ONE_20.
        int256 product = ONE_20;

        if (x >= x2) {
            x -= x2;
            product = (product * a2) / ONE_20;
        }
        if (x >= x3) {
            x -= x3;
            product = (product * a3) / ONE_20;
        }
        if (x >= x4) {
            x -= x4;
            product = (product * a4) / ONE_20;
        }
        if (x >= x5) {
            x -= x5;
            product = (product * a5) / ONE_20;
        }
        if (x >= x6) {
            x -= x6;
            product = (product * a6) / ONE_20;
        }
        if (x >= x7) {
            x -= x7;
            product = (product * a7) / ONE_20;
        }
        if (x >= x8) {
            x -= x8;
            product = (product * a8) / ONE_20;
        }
        if (x >= x9) {
            x -= x9;
            product = (product * a9) / ONE_20;
        }

        // x10 and x11 are unnecessary here since we have high enough precision already.

        // Now we need to compute e^x, where x is small (in particular, it is smaller than x9). We use the Taylor series
        // expansion for e^x: 1 + x + (x^2 / 2!) + (x^3 / 3!) + ... + (x^n / n!).

        int256 seriesSum = ONE_20; // The initial one in the sum, with 20 decimal places.
        int256 term; // Each term in the sum, where the nth term is (x^n / n!).

        // The first term is simply x.
        term = x;
        seriesSum += term;

        // Each term (x^n / n!) equals the previous one times x, divided by n. Since x is a fixed point number,
        // multiplying by it requires dividing by ONE_20, but dividing by the non-fixed point n values does not.

        term = ((term * x) / ONE_20) / 2;
        seriesSum += term;

        term = ((term * x) / ONE_20) / 3;
        seriesSum += term;

        term = ((term * x) / ONE_20) / 4;
        seriesSum += term;

        term = ((term * x) / ONE_20) / 5;
        seriesSum += term;

        term = ((term * x) / ONE_20) / 6;
        seriesSum += term;

        term = ((term * x) / ONE_20) / 7;
        seriesSum += term;

        term = ((term * x) / ONE_20) / 8;
        seriesSum += term;

        term = ((term * x) / ONE_20) / 9;
        seriesSum += term;

        term = ((term * x) / ONE_20) / 10;
        seriesSum += term;

        term = ((term * x) / ONE_20) / 11;
        seriesSum += term;

        term = ((term * x) / ONE_20) / 12;
        seriesSum += term;

        // 12 Taylor terms are sufficient for 18 decimal precision.

        // We now have the first a_n (with no decimals), and the product of all other a_n present, and the Taylor
        // approximation of the exponentiation of the remainder (both with 20 decimals). All that remains is to multiply
        // all three (one 20 decimal fixed point multiplication, dividing by ONE_20, and one integer multiplication),
        // and then drop two digits to return an 18 decimal value.

        return (((product * seriesSum) / ONE_20) * firstAN) / 100;
    }

    /**
     * @dev Logarithm (log(arg, base), with signed 18 decimal fixed point base and argument.
     */
    function log(int256 arg, int256 base) internal pure returns (int256) {
        // This performs a simple base change: log(arg, base) = ln(arg) / ln(base).

        // Both logBase and logArg are computed as 36 decimal fixed point numbers, either by using ln_36, or by
        // upscaling.

        int256 logBase;
        if (LN_36_LOWER_BOUND < base && base < LN_36_UPPER_BOUND) {
            logBase = _ln_36(base);
        } else {
            logBase = _ln(base) * ONE_18;
        }

        int256 logArg;
        if (LN_36_LOWER_BOUND < arg && arg < LN_36_UPPER_BOUND) {
            logArg = _ln_36(arg);
        } else {
            logArg = _ln(arg) * ONE_18;
        }

        // When dividing, we multiply by ONE_18 to arrive at a result with 18 decimal places
        return (logArg * ONE_18) / logBase;
    }

    /**
     * @dev Natural logarithm (ln(a)) with signed 18 decimal fixed point argument.
     */
    function ln(int256 a) internal pure returns (int256) {
        // The real natural logarithm is not defined for negative numbers or zero.
        _require(a > 0, Errors.OUT_OF_BOUNDS);
        if (LN_36_LOWER_BOUND < a && a < LN_36_UPPER_BOUND) {
            return _ln_36(a) / ONE_18;
        } else {
            return _ln(a);
        }
    }

    /**
     * @dev Internal natural logarithm (ln(a)) with signed 18 decimal fixed point argument.
     */
    function _ln(int256 a) private pure returns (int256) {
        if (a < ONE_18) {
            // Since ln(a^k) = k * ln(a), we can compute ln(a) as ln(a) = ln((1/a)^(-1)) = - ln((1/a)). If a is less
            // than one, 1/a will be greater than one, and this if statement will not be entered in the recursive call.
            // Fixed point division requires multiplying by ONE_18.
            return (-_ln((ONE_18 * ONE_18) / a));
        }

        // First, we use the fact that ln^(a * b) = ln(a) + ln(b) to decompose ln(a) into a sum of powers of two, which
        // we call x_n, where x_n == 2^(7 - n), which are the natural logarithm of precomputed quantities a_n (that is,
        // ln(a_n) = x_n). We choose the first x_n, x0, to equal 2^7 because the exponential of all larger powers cannot
        // be represented as 18 fixed point decimal numbers in 256 bits, and are therefore larger than a.
        // At the end of this process we will have the sum of all x_n = ln(a_n) that apply, and the remainder of this
        // decomposition, which will be lower than the smallest a_n.
        // ln(a) = k_0 * x_0 + k_1 * x_1 + ... + k_n * x_n + ln(remainder), where each k_n equals either 0 or 1.
        // We mutate a by subtracting a_n, making it the remainder of the decomposition.

        // For reasons related to how `exp` works, the first two a_n (e^(2^7) and e^(2^6)) are not stored as fixed point
        // numbers with 18 decimals, but instead as plain integers with 0 decimals, so we need to multiply them by
        // ONE_18 to convert them to fixed point.
        // For each a_n, we test if that term is present in the decomposition (if a is larger than it), and if so divide
        // by it and compute the accumulated sum.

        int256 sum = 0;
        if (a >= a0 * ONE_18) {
            a /= a0; // Integer, not fixed point division
            sum += x0;
        }

        if (a >= a1 * ONE_18) {
            a /= a1; // Integer, not fixed point division
            sum += x1;
        }

        // All other a_n and x_n are stored as 20 digit fixed point numbers, so we convert the sum and a to this format.
        sum *= 100;
        a *= 100;

        // Because further a_n are  20 digit fixed point numbers, we multiply by ONE_20 when dividing by them.

        if (a >= a2) {
            a = (a * ONE_20) / a2;
            sum += x2;
        }

        if (a >= a3) {
            a = (a * ONE_20) / a3;
            sum += x3;
        }

        if (a >= a4) {
            a = (a * ONE_20) / a4;
            sum += x4;
        }

        if (a >= a5) {
            a = (a * ONE_20) / a5;
            sum += x5;
        }

        if (a >= a6) {
            a = (a * ONE_20) / a6;
            sum += x6;
        }

        if (a >= a7) {
            a = (a * ONE_20) / a7;
            sum += x7;
        }

        if (a >= a8) {
            a = (a * ONE_20) / a8;
            sum += x8;
        }

        if (a >= a9) {
            a = (a * ONE_20) / a9;
            sum += x9;
        }

        if (a >= a10) {
            a = (a * ONE_20) / a10;
            sum += x10;
        }

        if (a >= a11) {
            a = (a * ONE_20) / a11;
            sum += x11;
        }

        // a is now a small number (smaller than a_11, which roughly equals 1.06). This means we can use a Taylor series
        // that converges rapidly for values of `a` close to one - the same one used in ln_36.
        // Let z = (a - 1) / (a + 1).
        // ln(a) = 2 * (z + z^3 / 3 + z^5 / 5 + z^7 / 7 + ... + z^(2 * n + 1) / (2 * n + 1))

        // Recall that 20 digit fixed point division requires multiplying by ONE_20, and multiplication requires
        // division by ONE_20.
        int256 z = ((a - ONE_20) * ONE_20) / (a + ONE_20);
        int256 z_squared = (z * z) / ONE_20;

        // num is the numerator of the series: the z^(2 * n + 1) term
        int256 num = z;

        // seriesSum holds the accumulated sum of each term in the series, starting with the initial z
        int256 seriesSum = num;

        // In each step, the numerator is multiplied by z^2
        num = (num * z_squared) / ONE_20;
        seriesSum += num / 3;

        num = (num * z_squared) / ONE_20;
        seriesSum += num / 5;

        num = (num * z_squared) / ONE_20;
        seriesSum += num / 7;

        num = (num * z_squared) / ONE_20;
        seriesSum += num / 9;

        num = (num * z_squared) / ONE_20;
        seriesSum += num / 11;

        // 6 Taylor terms are sufficient for 36 decimal precision.

        // Finally, we multiply by 2 (non fixed point) to compute ln(remainder)
        seriesSum *= 2;

        // We now have the sum of all x_n present, and the Taylor approximation of the logarithm of the remainder (both
        // with 20 decimals). All that remains is to sum these two, and then drop two digits to return a 18 decimal
        // value.

        return (sum + seriesSum) / 100;
    }

    /**
     * @dev Intrnal high precision (36 decimal places) natural logarithm (ln(x)) with signed 18 decimal fixed point argument,
     * for x close to one.
     *
     * Should only be used if x is between LN_36_LOWER_BOUND and LN_36_UPPER_BOUND.
     */
    function _ln_36(int256 x) private pure returns (int256) {
        // Since ln(1) = 0, a value of x close to one will yield a very small result, which makes using 36 digits
        // worthwhile.

        // First, we transform x to a 36 digit fixed point value.
        x *= ONE_18;

        // We will use the following Taylor expansion, which converges very rapidly. Let z = (x - 1) / (x + 1).
        // ln(x) = 2 * (z + z^3 / 3 + z^5 / 5 + z^7 / 7 + ... + z^(2 * n + 1) / (2 * n + 1))

        // Recall that 36 digit fixed point division requires multiplying by ONE_36, and multiplication requires
        // division by ONE_36.
        int256 z = ((x - ONE_36) * ONE_36) / (x + ONE_36);
        int256 z_squared = (z * z) / ONE_36;

        // num is the numerator of the series: the z^(2 * n + 1) term
        int256 num = z;

        // seriesSum holds the accumulated sum of each term in the series, starting with the initial z
        int256 seriesSum = num;

        // In each step, the numerator is multiplied by z^2
        num = (num * z_squared) / ONE_36;
        seriesSum += num / 3;

        num = (num * z_squared) / ONE_36;
        seriesSum += num / 5;

        num = (num * z_squared) / ONE_36;
        seriesSum += num / 7;

        num = (num * z_squared) / ONE_36;
        seriesSum += num / 9;

        num = (num * z_squared) / ONE_36;
        seriesSum += num / 11;

        num = (num * z_squared) / ONE_36;
        seriesSum += num / 13;

        num = (num * z_squared) / ONE_36;
        seriesSum += num / 15;

        // 8 Taylor terms are sufficient for 36 decimal precision.

        // All that remains is multiplying by 2 (non fixed point).
        return seriesSum * 2;
    }
}

// File: contracts/balancer-core-v2/lib/math/FixedPoint.sol



// SPDX-License-Identifier: GPL-3.0-or-later
// This program is free software: you can redistribute it and/or modify
// it under the terms of the GNU General Public License as published by
// the Free Software Foundation, either version 3 of the License, or
// (at your option) any later version.

// This program is distributed in the hope that it will be useful,
// but WITHOUT ANY WARRANTY; without even the implied warranty of
// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
// GNU General Public License for more details.

// You should have received a copy of the GNU General Public License
// along with this program.  If not, see <http://www.gnu.org/licenses/>.

pragma solidity ^0.7.0;

import "./LogExpMath.sol";
import "../helpers/BalancerErrors.sol";

/* solhint-disable private-vars-leading-underscore */

library FixedPoint {
    uint256 internal constant ONE = 1e18; // 18 decimal places
    uint256 internal constant MAX_POW_RELATIVE_ERROR = 10000; // 10^(-14)

    // Minimum base for the power function when the exponent is 'free' (larger than ONE).
    uint256 internal constant MIN_POW_BASE_FREE_EXPONENT = 0.7e18;

    function add(uint256 a, uint256 b) internal pure returns (uint256) {
        // Fixed Point addition is the same as regular checked addition

        uint256 c = a + b;
        _require(c >= a, Errors.ADD_OVERFLOW);
        return c;
    }

    function sub(uint256 a, uint256 b) internal pure returns (uint256) {
        // Fixed Point addition is the same as regular checked addition

        _require(b <= a, Errors.SUB_OVERFLOW);
        uint256 c = a - b;
        return c;
    }

    function mulDown(uint256 a, uint256 b) internal pure returns (uint256) {
        uint256 product = a * b;
        _require(a == 0 || product / a == b, Errors.MUL_OVERFLOW);

        return product / ONE;
    }

    function mulUp(uint256 a, uint256 b) internal pure returns (uint256) {
        uint256 product = a * b;
        _require(a == 0 || product / a == b, Errors.MUL_OVERFLOW);

        if (product == 0) {
            return 0;
        } else {
            // The traditional divUp formula is:
            // divUp(x, y) := (x + y - 1) / y
            // To avoid intermediate overflow in the addition, we distribute the division and get:
            // divUp(x, y) := (x - 1) / y + 1
            // Note that this requires x != 0, which we already tested for.

            return ((product - 1) / ONE) + 1;
        }
    }

    function divDown(uint256 a, uint256 b) internal pure returns (uint256) {
        _require(b != 0, Errors.ZERO_DIVISION);

        if (a == 0) {
            return 0;
        } else {
            uint256 aInflated = a * ONE;
            _require(aInflated / a == ONE, Errors.DIV_INTERNAL); // mul overflow

            return aInflated / b;
        }
    }

    function divUp(uint256 a, uint256 b) internal pure returns (uint256) {
        _require(b != 0, Errors.ZERO_DIVISION);

        if (a == 0) {
            return 0;
        } else {
            uint256 aInflated = a * ONE;
            _require(aInflated / a == ONE, Errors.DIV_INTERNAL); // mul overflow

            // The traditional divUp formula is:
            // divUp(x, y) := (x + y - 1) / y
            // To avoid intermediate overflow in the addition, we distribute the division and get:
            // divUp(x, y) := (x - 1) / y + 1
            // Note that this requires x != 0, which we already tested for.

            return ((aInflated - 1) / b) + 1;
        }
    }

    /**
     * @dev Returns x^y, assuming both are fixed point numbers, rounding down. The result is guaranteed to not be above
     * the true value (that is, the error function expected - actual is always positive).
     */
    function powDown(uint256 x, uint256 y) internal pure returns (uint256) {
        uint256 raw = LogExpMath.pow(x, y);
        uint256 maxError = add(mulUp(raw, MAX_POW_RELATIVE_ERROR), 1);

        if (raw < maxError) {
            return 0;
        } else {
            return sub(raw, maxError);
        }
    }

    /**
     * @dev Returns x^y, assuming both are fixed point numbers, rounding up. The result is guaranteed to not be below
     * the true value (that is, the error function expected - actual is always negative).
     */
    function powUp(uint256 x, uint256 y) internal pure returns (uint256) {
        uint256 raw = LogExpMath.pow(x, y);
        uint256 maxError = add(mulUp(raw, MAX_POW_RELATIVE_ERROR), 1);

        return add(raw, maxError);
    }

    /**
     * @dev Returns the complement of a value (1 - x), capped to 0 if x is larger than 1.
     *
     * Useful when computing the complement for values with some level of relative error, as it strips this error and
     * prevents intermediate negative values.
     */
    function complement(uint256 x) internal pure returns (uint256) {
        return (x < ONE) ? (ONE - x) : 0;
    }
}

// File: contracts/balancer-core-v2/vault/interfaces/IMinimalSwapInfoPool.sol



// SPDX-License-Identifier: GPL-3.0-or-later
// This program is free software: you can redistribute it and/or modify
// it under the terms of the GNU General Public License as published by
// the Free Software Foundation, either version 3 of the License, or
// (at your option) any later version.

// This program is distributed in the hope that it will be useful,
// but WITHOUT ANY WARRANTY; without even the implied warranty of
// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
// GNU General Public License for more details.

// You should have received a copy of the GNU General Public License
// along with this program.  If not, see <http://www.gnu.org/licenses/>.

pragma solidity ^0.7.0;
pragma experimental ABIEncoderV2;

import "./IBasePool.sol";

/**
 * @dev Pool contracts with the MinimalSwapInfo or TwoToken specialization settings should implement this interface.
 *
 * This is called by the Vault when a user calls `IVault.swap` or `IVault.batchSwap` to swap with this Pool.
 * Returns the number of tokens the Pool will grant to the user in a 'given in' swap, or that the user will grant
 * to the pool in a 'given out' swap.
 *
 * This can often be implemented by a `view` function, since many pricing algorithms don't need to track state
 * changes in swaps. However, contracts implementing this in non-view functions should check that the caller is
 * indeed the Vault.
 */
interface IMinimalSwapInfoPool is IBasePool {
    function onSwap(
        SwapRequest memory swapRequest,
        uint256 currentBalanceTokenIn,
        uint256 currentBalanceTokenOut
    ) external returns (uint256 amount);
}

// File: contracts/balancer-core-v2/vault/interfaces/IVault.sol



// SPDX-License-Identifier: GPL-3.0-or-later
// This program is free software: you can redistribute it and/or modify
// it under the terms of the GNU General Public License as published by
// the Free Software Foundation, either version 3 of the License, or
// (at your option) any later version.

// This program is distributed in the hope that it will be useful,
// but WITHOUT ANY WARRANTY; without even the implied warranty of
// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
// GNU General Public License for more details.

// You should have received a copy of the GNU General Public License
// along with this program.  If not, see <http://www.gnu.org/licenses/>.

pragma experimental ABIEncoderV2;

import "../../lib/openzeppelin/IERC20.sol";

import "./IWETH.sol";
import "./IAsset.sol";
import "./IAuthorizer.sol";
import "./IFlashLoanRecipient.sol";
import "../ProtocolFeesCollector.sol";

import "../../lib/helpers/ISignaturesValidator.sol";
import "../../lib/helpers/ITemporarilyPausable.sol";

pragma solidity ^0.7.0;

/**
 * @dev Full external interface for the Vault core contract - no external or public methods exist in the contract that
 * don't override one of these declarations.
 */
interface IVault is ISignaturesValidator, ITemporarilyPausable {
    // Generalities about the Vault:
    //
    // - Whenever documentation refers to 'tokens', it strictly refers to ERC20-compliant token contracts. Tokens are
    // transferred out of the Vault by calling the `IERC20.transfer` function, and transferred in by calling
    // `IERC20.transferFrom`. In these cases, the sender must have previously allowed the Vault to use their tokens by
    // calling `IERC20.approve`. The only deviation from the ERC20 standard that is supported is functions not returning
    // a boolean value: in these scenarios, a non-reverting call is assumed to be successful.
    //
    // - All non-view functions in the Vault are non-reentrant: calling them while another one is mid-execution (e.g.
    // while execution control is transferred to a token contract during a swap) will result in a revert. View
    // functions can be called in a re-reentrant way, but doing so might cause them to return inconsistent results.
    // Contracts calling view functions in the Vault must make sure the Vault has not already been entered.
    //
    // - View functions revert if referring to either unregistered Pools, or unregistered tokens for registered Pools.

    // Authorizer
    //
    // Some system actions are permissioned, like setting and collecting protocol fees. This permissioning system exists
    // outside of the Vault in the Authorizer contract: the Vault simply calls the Authorizer to check if the caller
    // can perform a given action.

    /**
     * @dev Returns the Vault's Authorizer.
     */
    function getAuthorizer() external view returns (IAuthorizer);

    /**
     * @dev Sets a new Authorizer for the Vault. The caller must be allowed by the current Authorizer to do this.
     *
     * Emits an `AuthorizerChanged` event.
     */
    function setAuthorizer(IAuthorizer newAuthorizer) external;

    /**
     * @dev Emitted when a new authorizer is set by `setAuthorizer`.
     */
    event AuthorizerChanged(IAuthorizer indexed newAuthorizer);

    // Relayers
    //
    // Additionally, it is possible for an account to perform certain actions on behalf of another one, using their
    // Vault ERC20 allowance and Internal Balance. These accounts are said to be 'relayers' for these Vault functions,
    // and are expected to be smart contracts with sound authentication mechanisms. For an account to be able to wield
    // this power, two things must occur:
    //  - The Authorizer must grant the account the permission to be a relayer for the relevant Vault function. This
    //    means that Balancer governance must approve each individual contract to act as a relayer for the intended
    //    functions.
    //  - Each user must approve the relayer to act on their behalf.
    // This double protection means users cannot be tricked into approving malicious relayers (because they will not
    // have been allowed by the Authorizer via governance), nor can malicious relayers approved by a compromised
    // Authorizer or governance drain user funds, since they would also need to be approved by each individual user.

    /**
     * @dev Returns true if `user` has approved `relayer` to act as a relayer for them.
     */
    function hasApprovedRelayer(address user, address relayer) external view returns (bool);

    /**
     * @dev Allows `relayer` to act as a relayer for `sender` if `approved` is true, and disallows it otherwise.
     *
     * Emits a `RelayerApprovalChanged` event.
     */
    function setRelayerApproval(
        address sender,
        address relayer,
        bool approved
    ) external;

    /**
     * @dev Emitted every time a relayer is approved or disapproved by `setRelayerApproval`.
     */
    event RelayerApprovalChanged(address indexed relayer, address indexed sender, bool approved);

    // Internal Balance
    //
    // Users can deposit tokens into the Vault, where they are allocated to their Internal Balance, and later
    // transferred or withdrawn. It can also be used as a source of tokens when joining Pools, as a destination
    // when exiting them, and as either when performing swaps. This usage of Internal Balance results in greatly reduced
    // gas costs when compared to relying on plain ERC20 transfers, leading to large savings for frequent users.
    //
    // Internal Balance management features batching, which means a single contract call can be used to perform multiple
    // operations of different kinds, with different senders and recipients, at once.

    /**
     * @dev Returns `user`'s Internal Balance for a set of tokens.
     */
    function getInternalBalance(address user, IERC20[] memory tokens) external view returns (uint256[] memory);

    /**
     * @dev Performs a set of user balance operations, which involve Internal Balance (deposit, withdraw or transfer)
     * and plain ERC20 transfers using the Vault's allowance. This last feature is particularly useful for relayers, as
     * it lets integrators reuse a user's Vault allowance.
     *
     * For each operation, if the caller is not `sender`, it must be an authorized relayer for them.
     */
    function manageUserBalance(UserBalanceOp[] memory ops) external payable;

    /**
     * @dev Data for `manageUserBalance` operations, which include the possibility for ETH to be sent and received
     without manual WETH wrapping or unwrapping.
     */
    struct UserBalanceOp {
        UserBalanceOpKind kind;
        IAsset asset;
        uint256 amount;
        address sender;
        address payable recipient;
    }

    // There are four possible operations in `manageUserBalance`:
    //
    // - DEPOSIT_INTERNAL
    // Increases the Internal Balance of the `recipient` account by transferring tokens from the corresponding
    // `sender`. The sender must have allowed the Vault to use their tokens via `IERC20.approve()`.
    //
    // ETH can be used by passing the ETH sentinel value as the asset and forwarding ETH in the call: it will be wrapped
    // and deposited as WETH. Any ETH amount remaining will be sent back to the caller (not the sender, which is
    // relevant for relayers).
    //
    // Emits an `InternalBalanceChanged` event.
    //
    //
    // - WITHDRAW_INTERNAL
    // Decreases the Internal Balance of the `sender` account by transferring tokens to the `recipient`.
    //
    // ETH can be used by passing the ETH sentinel value as the asset. This will deduct WETH instead, unwrap it and send
    // it to the recipient as ETH.
    //
    // Emits an `InternalBalanceChanged` event.
    //
    //
    // - TRANSFER_INTERNAL
    // Transfers tokens from the Internal Balance of the `sender` account to the Internal Balance of `recipient`.
    //
    // Reverts if the ETH sentinel value is passed.
    //
    // Emits an `InternalBalanceChanged` event.
    //
    //
    // - TRANSFER_EXTERNAL
    // Transfers tokens from `sender` to `recipient`, using the Vault's ERC20 allowance. This is typically used by
    // relayers, as it lets them reuse a user's Vault allowance.
    //
    // Reverts if the ETH sentinel value is passed.
    //
    // Emits an `ExternalBalanceTransfer` event.

    enum UserBalanceOpKind { DEPOSIT_INTERNAL, WITHDRAW_INTERNAL, TRANSFER_INTERNAL, TRANSFER_EXTERNAL }

    /**
     * @dev Emitted when a user's Internal Balance changes, either from calls to `manageUserBalance`, or through
     * interacting with Pools using Internal Balance.
     *
     * Because Internal Balance works exclusively with ERC20 tokens, ETH deposits and withdrawals will use the WETH
     * address.
     */
    event InternalBalanceChanged(address indexed user, IERC20 indexed token, int256 delta);

    /**
     * @dev Emitted when a user's Vault ERC20 allowance is used by the Vault to transfer tokens to an external account.
     */
    event ExternalBalanceTransfer(IERC20 indexed token, address indexed sender, address recipient, uint256 amount);

    // Pools
    //
    // There are three specialization settings for Pools, which allow for cheaper swaps at the cost of reduced
    // functionality:
    //
    //  - General: no specialization, suited for all Pools. IGeneralPool is used for swap request callbacks, passing the
    // balance of all tokens in the Pool. These Pools have the largest swap costs (because of the extra storage reads),
    // which increase with the number of registered tokens.
    //
    //  - Minimal Swap Info: IMinimalSwapInfoPool is used instead of IGeneralPool, which saves gas by only passing the
    // balance of the two tokens involved in the swap. This is suitable for some pricing algorithms, like the weighted
    // constant product one popularized by Balancer V1. Swap costs are smaller compared to general Pools, and are
    // independent of the number of registered tokens.
    //
    //  - Two Token: only allows two tokens to be registered. This achieves the lowest possible swap gas cost. Like
    // minimal swap info Pools, these are called via IMinimalSwapInfoPool.

    enum PoolSpecialization { GENERAL, MINIMAL_SWAP_INFO, TWO_TOKEN }

    /**
     * @dev Registers the caller account as a Pool with a given specialization setting. Returns the Pool's ID, which
     * is used in all Pool-related functions. Pools cannot be deregistered, nor can the Pool's specialization be
     * changed.
     *
     * The caller is expected to be a smart contract that implements either `IGeneralPool` or `IMinimalSwapInfoPool`,
     * depending on the chosen specialization setting. This contract is known as the Pool's contract.
     *
     * Note that the same contract may register itself as multiple Pools with unique Pool IDs, or in other words,
     * multiple Pools may share the same contract.
     *
     * Emits a `PoolRegistered` event.
     */
    function registerPool(PoolSpecialization specialization) external returns (bytes32);

    /**
     * @dev Emitted when a Pool is registered by calling `registerPool`.
     */
    event PoolRegistered(bytes32 indexed poolId, address indexed poolAddress, PoolSpecialization specialization);

    /**
     * @dev Returns a Pool's contract address and specialization setting.
     */
    function getPool(bytes32 poolId) external view returns (address, PoolSpecialization);

    /**
     * @dev Registers `tokens` for the `poolId` Pool. Must be called by the Pool's contract.
     *
     * Pools can only interact with tokens they have registered. Users join a Pool by transferring registered tokens,
     * exit by receiving registered tokens, and can only swap registered tokens.
     *
     * Each token can only be registered once. For Pools with the Two Token specialization, `tokens` must have a length
     * of two, that is, both tokens must be registered in the same `registerTokens` call, and they must be sorted in
     * ascending order.
     *
     * The `tokens` and `assetManagers` arrays must have the same length, and each entry in these indicates the Asset
     * Manager for the corresponding token. Asset Managers can manage a Pool's tokens via `managePoolBalance`,
     * depositing and withdrawing them directly, and can even set their balance to arbitrary amounts. They are therefore
     * expected to be highly secured smart contracts with sound design principles, and the decision to register an
     * Asset Manager should not be made lightly.
     *
     * Pools can choose not to assign an Asset Manager to a given token by passing in the zero address. Once an Asset
     * Manager is set, it cannot be changed except by deregistering the associated token and registering again with a
     * different Asset Manager.
     *
     * Emits a `TokensRegistered` event.
     */
    function registerTokens(
        bytes32 poolId,
        IERC20[] memory tokens,
        address[] memory assetManagers
    ) external;

    /**
     * @dev Emitted when a Pool registers tokens by calling `registerTokens`.
     */
    event TokensRegistered(bytes32 indexed poolId, IERC20[] tokens, address[] assetManagers);

    /**
     * @dev Deregisters `tokens` for the `poolId` Pool. Must be called by the Pool's contract.
     *
     * Only registered tokens (via `registerTokens`) can be deregistered. Additionally, they must have zero total
     * balance. For Pools with the Two Token specialization, `tokens` must have a length of two, that is, both tokens
     * must be deregistered in the same `deregisterTokens` call.
     *
     * A deregistered token can be re-registered later on, possibly with a different Asset Manager.
     *
     * Emits a `TokensDeregistered` event.
     */
    function deregisterTokens(bytes32 poolId, IERC20[] memory tokens) external;

    /**
     * @dev Emitted when a Pool deregisters tokens by calling `deregisterTokens`.
     */
    event TokensDeregistered(bytes32 indexed poolId, IERC20[] tokens);

    /**
     * @dev Returns detailed information for a Pool's registered token.
     *
     * `cash` is the number of tokens the Vault currently holds for the Pool. `managed` is the number of tokens
     * withdrawn and held outside the Vault by the Pool's token Asset Manager. The Pool's total balance for `token`
     * equals the sum of `cash` and `managed`.
     *
     * Internally, `cash` and `managed` are stored using 112 bits. No action can ever cause a Pool's token `cash`,
     * `managed` or `total` balance to be greater than 2^112 - 1.
     *
     * `lastChangeBlock` is the number of the block in which `token`'s total balance was last modified (via either a
     * join, exit, swap, or Asset Manager update). This value is useful to avoid so-called 'sandwich attacks', for
     * example when developing price oracles. A change of zero (e.g. caused by a swap with amount zero) is considered a
     * change for this purpose, and will update `lastChangeBlock`.
     *
     * `assetManager` is the Pool's token Asset Manager.
     */
    function getPoolTokenInfo(bytes32 poolId, IERC20 token)
        external
        view
        returns (
            uint256 cash,
            uint256 managed,
            uint256 lastChangeBlock,
            address assetManager
        );

    /**
     * @dev Returns a Pool's registered tokens, the total balance for each, and the latest block when *any* of
     * the tokens' `balances` changed.
     *
     * The order of the `tokens` array is the same order that will be used in `joinPool`, `exitPool`, as well as in all
     * Pool hooks (where applicable). Calls to `registerTokens` and `deregisterTokens` may change this order.
     *
     * If a Pool only registers tokens once, and these are sorted in ascending order, they will be stored in the same
     * order as passed to `registerTokens`.
     *
     * Total balances include both tokens held by the Vault and those withdrawn by the Pool's Asset Managers. These are
     * the amounts used by joins, exits and swaps. For a detailed breakdown of token balances, use `getPoolTokenInfo`
     * instead.
     */
    function getPoolTokens(bytes32 poolId)
        external
        view
        returns (
            IERC20[] memory tokens,
            uint256[] memory balances,
            uint256 lastChangeBlock
        );

    /**
     * @dev Called by users to join a Pool, which transfers tokens from `sender` into the Pool's balance. This will
     * trigger custom Pool behavior, which will typically grant something in return to `recipient` - often tokenized
     * Pool shares.
     *
     * If the caller is not `sender`, it must be an authorized relayer for them.
     *
     * The `assets` and `maxAmountsIn` arrays must have the same length, and each entry indicates the maximum amount
     * to send for each asset. The amounts to send are decided by the Pool and not the Vault: it just enforces
     * these maximums.
     *
     * If joining a Pool that holds WETH, it is possible to send ETH directly: the Vault will do the wrapping. To enable
     * this mechanism, the IAsset sentinel value (the zero address) must be passed in the `assets` array instead of the
     * WETH address. Note that it is not possible to combine ETH and WETH in the same join. Any excess ETH will be sent
     * back to the caller (not the sender, which is important for relayers).
     *
     * `assets` must have the same length and order as the array returned by `getPoolTokens`. This prevents issues when
     * interacting with Pools that register and deregister tokens frequently. If sending ETH however, the array must be
     * sorted *before* replacing the WETH address with the ETH sentinel value (the zero address), which means the final
     * `assets` array might not be sorted. Pools with no registered tokens cannot be joined.
     *
     * If `fromInternalBalance` is true, the caller's Internal Balance will be preferred: ERC20 transfers will only
     * be made for the difference between the requested amount and Internal Balance (if any). Note that ETH cannot be
     * withdrawn from Internal Balance: attempting to do so will trigger a revert.
     *
     * This causes the Vault to call the `IBasePool.onJoinPool` hook on the Pool's contract, where Pools implement
     * their own custom logic. This typically requires additional information from the user (such as the expected number
     * of Pool shares). This can be encoded in the `userData` argument, which is ignored by the Vault and passed
     * directly to the Pool's contract, as is `recipient`.
     *
     * Emits a `PoolBalanceChanged` event.
     */
    function joinPool(
        bytes32 poolId,
        address sender,
        address recipient,
        JoinPoolRequest memory request
    ) external payable;

    struct JoinPoolRequest {
        IAsset[] assets;
        uint256[] maxAmountsIn;
        bytes userData;
        bool fromInternalBalance;
    }

    /**
     * @dev Called by users to exit a Pool, which transfers tokens from the Pool's balance to `recipient`. This will
     * trigger custom Pool behavior, which will typically ask for something in return from `sender` - often tokenized
     * Pool shares. The amount of tokens that can be withdrawn is limited by the Pool's `cash` balance (see
     * `getPoolTokenInfo`).
     *
     * If the caller is not `sender`, it must be an authorized relayer for them.
     *
     * The `tokens` and `minAmountsOut` arrays must have the same length, and each entry in these indicates the minimum
     * token amount to receive for each token contract. The amounts to send are decided by the Pool and not the Vault:
     * it just enforces these minimums.
     *
     * If exiting a Pool that holds WETH, it is possible to receive ETH directly: the Vault will do the unwrapping. To
     * enable this mechanism, the IAsset sentinel value (the zero address) must be passed in the `assets` array instead
     * of the WETH address. Note that it is not possible to combine ETH and WETH in the same exit.
     *
     * `assets` must have the same length and order as the array returned by `getPoolTokens`. This prevents issues when
     * interacting with Pools that register and deregister tokens frequently. If receiving ETH however, the array must
     * be sorted *before* replacing the WETH address with the ETH sentinel value (the zero address), which means the
     * final `assets` array might not be sorted. Pools with no registered tokens cannot be exited.
     *
     * If `toInternalBalance` is true, the tokens will be deposited to `recipient`'s Internal Balance. Otherwise,
     * an ERC20 transfer will be performed. Note that ETH cannot be deposited to Internal Balance: attempting to
     * do so will trigger a revert.
     *
     * `minAmountsOut` is the minimum amount of tokens the user expects to get out of the Pool, for each token in the
     * `tokens` array. This array must match the Pool's registered tokens.
     *
     * This causes the Vault to call the `IBasePool.onExitPool` hook on the Pool's contract, where Pools implement
     * their own custom logic. This typically requires additional information from the user (such as the expected number
     * of Pool shares to return). This can be encoded in the `userData` argument, which is ignored by the Vault and
     * passed directly to the Pool's contract.
     *
     * Emits a `PoolBalanceChanged` event.
     */
    function exitPool(
        bytes32 poolId,
        address sender,
        address payable recipient,
        ExitPoolRequest memory request
    ) external;

    struct ExitPoolRequest {
        IAsset[] assets;
        uint256[] minAmountsOut;
        bytes userData;
        bool toInternalBalance;
    }

    /**
     * @dev Emitted when a user joins or exits a Pool by calling `joinPool` or `exitPool`, respectively.
     */
    event PoolBalanceChanged(
        bytes32 indexed poolId,
        address indexed liquidityProvider,
        IERC20[] tokens,
        int256[] deltas,
        uint256[] protocolFeeAmounts
    );

    enum PoolBalanceChangeKind { JOIN, EXIT }

    // Swaps
    //
    // Users can swap tokens with Pools by calling the `swap` and `batchSwap` functions. To do this,
    // they need not trust Pool contracts in any way: all security checks are made by the Vault. They must however be
    // aware of the Pools' pricing algorithms in order to estimate the prices Pools will quote.
    //
    // The `swap` function executes a single swap, while `batchSwap` can perform multiple swaps in sequence.
    // In each individual swap, tokens of one kind are sent from the sender to the Pool (this is the 'token in'),
    // and tokens of another kind are sent from the Pool to the recipient in exchange (this is the 'token out').
    // More complex swaps, such as one token in to multiple tokens out can be achieved by batching together
    // individual swaps.
    //
    // There are two swap kinds:
    //  - 'given in' swaps, where the amount of tokens in (sent to the Pool) is known, and the Pool determines (via the
    // `onSwap` hook) the amount of tokens out (to send to the recipient).
    //  - 'given out' swaps, where the amount of tokens out (received from the Pool) is known, and the Pool determines
    // (via the `onSwap` hook) the amount of tokens in (to receive from the sender).
    //
    // Additionally, it is possible to chain swaps using a placeholder input amount, which the Vault replaces with
    // the calculated output of the previous swap. If the previous swap was 'given in', this will be the calculated
    // tokenOut amount. If the previous swap was 'given out', it will use the calculated tokenIn amount. These extended
    // swaps are known as 'multihop' swaps, since they 'hop' through a number of intermediate tokens before arriving at
    // the final intended token.
    //
    // In all cases, tokens are only transferred in and out of the Vault (or withdrawn from and deposited into Internal
    // Balance) after all individual swaps have been completed, and the net token balance change computed. This makes
    // certain swap patterns, such as multihops, or swaps that interact with the same token pair in multiple Pools, cost
    // much less gas than they would otherwise.
    //
    // It also means that under certain conditions it is possible to perform arbitrage by swapping with multiple
    // Pools in a way that results in net token movement out of the Vault (profit), with no tokens being sent in (only
    // updating the Pool's internal accounting).
    //
    // To protect users from front-running or the market changing rapidly, they supply a list of 'limits' for each token
    // involved in the swap, where either the maximum number of tokens to send (by passing a positive value) or the
    // minimum amount of tokens to receive (by passing a negative value) is specified.
    //
    // Additionally, a 'deadline' timestamp can also be provided, forcing the swap to fail if it occurs after
    // this point in time (e.g. if the transaction failed to be included in a block promptly).
    //
    // If interacting with Pools that hold WETH, it is possible to both send and receive ETH directly: the Vault will do
    // the wrapping and unwrapping. To enable this mechanism, the IAsset sentinel value (the zero address) must be
    // passed in the `assets` array instead of the WETH address. Note that it is possible to combine ETH and WETH in the
    // same swap. Any excess ETH will be sent back to the caller (not the sender, which is relevant for relayers).
    //
    // Finally, Internal Balance can be used when either sending or receiving tokens.

    enum SwapKind { GIVEN_IN, GIVEN_OUT }

    /**
     * @dev Performs a swap with a single Pool.
     *
     * If the swap is 'given in' (the number of tokens to send to the Pool is known), it returns the amount of tokens
     * taken from the Pool, which must be greater than or equal to `limit`.
     *
     * If the swap is 'given out' (the number of tokens to take from the Pool is known), it returns the amount of tokens
     * sent to the Pool, which must be less than or equal to `limit`.
     *
     * Internal Balance usage and the recipient are determined by the `funds` struct.
     *
     * Emits a `Swap` event.
     */
    function swap(
        SingleSwap memory singleSwap,
        FundManagement memory funds,
        uint256 limit,
        uint256 deadline
    ) external payable returns (uint256);

    /**
     * @dev Data for a single swap executed by `swap`. `amount` is either `amountIn` or `amountOut` depending on
     * the `kind` value.
     *
     * `assetIn` and `assetOut` are either token addresses, or the IAsset sentinel value for ETH (the zero address).
     * Note that Pools never interact with ETH directly: it will be wrapped to or unwrapped from WETH by the Vault.
     *
     * The `userData` field is ignored by the Vault, but forwarded to the Pool in the `onSwap` hook, and may be
     * used to extend swap behavior.
     */
    struct SingleSwap {
        bytes32 poolId;
        SwapKind kind;
        IAsset assetIn;
        IAsset assetOut;
        uint256 amount;
        bytes userData;
    }

    /**
     * @dev Performs a series of swaps with one or multiple Pools. In each individual swap, the caller determines either
     * the amount of tokens sent to or received from the Pool, depending on the `kind` value.
     *
     * Returns an array with the net Vault asset balance deltas. Positive amounts represent tokens (or ETH) sent to the
     * Vault, and negative amounts represent tokens (or ETH) sent by the Vault. Each delta corresponds to the asset at
     * the same index in the `assets` array.
     *
     * Swaps are executed sequentially, in the order specified by the `swaps` array. Each array element describes a
     * Pool, the token to be sent to this Pool, the token to receive from it, and an amount that is either `amountIn` or
     * `amountOut` depending on the swap kind.
     *
     * Multihop swaps can be executed by passing an `amount` value of zero for a swap. This will cause the amount in/out
     * of the previous swap to be used as the amount in for the current one. In a 'given in' swap, 'tokenIn' must equal
     * the previous swap's `tokenOut`. For a 'given out' swap, `tokenOut` must equal the previous swap's `tokenIn`.
     *
     * The `assets` array contains the addresses of all assets involved in the swaps. These are either token addresses,
     * or the IAsset sentinel value for ETH (the zero address). Each entry in the `swaps` array specifies tokens in and
     * out by referencing an index in `assets`. Note that Pools never interact with ETH directly: it will be wrapped to
     * or unwrapped from WETH by the Vault.
     *
     * Internal Balance usage, sender, and recipient are determined by the `funds` struct. The `limits` array specifies
     * the minimum or maximum amount of each token the vault is allowed to transfer.
     *
     * `batchSwap` can be used to make a single swap, like `swap` does, but doing so requires more gas than the
     * equivalent `swap` call.
     *
     * Emits `Swap` events.
     */
    function batchSwap(
        SwapKind kind,
        BatchSwapStep[] memory swaps,
        IAsset[] memory assets,
        FundManagement memory funds,
        int256[] memory limits,
        uint256 deadline
    ) external payable returns (int256[] memory);

    /**
     * @dev Data for each individual swap executed by `batchSwap`. The asset in and out fields are indexes into the
     * `assets` array passed to that function, and ETH assets are converted to WETH.
     *
     * If `amount` is zero, the multihop mechanism is used to determine the actual amount based on the amount in/out
     * from the previous swap, depending on the swap kind.
     *
     * The `userData` field is ignored by the Vault, but forwarded to the Pool in the `onSwap` hook, and may be
     * used to extend swap behavior.
     */
    struct BatchSwapStep {
        bytes32 poolId;
        uint256 assetInIndex;
        uint256 assetOutIndex;
        uint256 amount;
        bytes userData;
    }

    /**
     * @dev Emitted for each individual swap performed by `swap` or `batchSwap`.
     */
    event Swap(
        bytes32 indexed poolId,
        IERC20 indexed tokenIn,
        IERC20 indexed tokenOut,
        uint256 amountIn,
        uint256 amountOut
    );

    /**
     * @dev All tokens in a swap are either sent from the `sender` account to the Vault, or from the Vault to the
     * `recipient` account.
     *
     * If the caller is not `sender`, it must be an authorized relayer for them.
     *
     * If `fromInternalBalance` is true, the `sender`'s Internal Balance will be preferred, performing an ERC20
     * transfer for the difference between the requested amount and the User's Internal Balance (if any). The `sender`
     * must have allowed the Vault to use their tokens via `IERC20.approve()`. This matches the behavior of
     * `joinPool`.
     *
     * If `toInternalBalance` is true, tokens will be deposited to `recipient`'s internal balance instead of
     * transferred. This matches the behavior of `exitPool`.
     *
     * Note that ETH cannot be deposited to or withdrawn from Internal Balance: attempting to do so will trigger a
     * revert.
     */
    struct FundManagement {
        address sender;
        bool fromInternalBalance;
        address payable recipient;
        bool toInternalBalance;
    }

    /**
     * @dev Simulates a call to `batchSwap`, returning an array of Vault asset deltas. Calls to `swap` cannot be
     * simulated directly, but an equivalent `batchSwap` call can and will yield the exact same result.
     *
     * Each element in the array corresponds to the asset at the same index, and indicates the number of tokens (or ETH)
     * the Vault would take from the sender (if positive) or send to the recipient (if negative). The arguments it
     * receives are the same that an equivalent `batchSwap` call would receive.
     *
     * Unlike `batchSwap`, this function performs no checks on the sender or recipient field in the `funds` struct.
     * This makes it suitable to be called by off-chain applications via eth_call without needing to hold tokens,
     * approve them for the Vault, or even know a user's address.
     *
     * Note that this function is not 'view' (due to implementation details): the client code must explicitly execute
     * eth_call instead of eth_sendTransaction.
     */
    function queryBatchSwap(
        SwapKind kind,
        BatchSwapStep[] memory swaps,
        IAsset[] memory assets,
        FundManagement memory funds
    ) external returns (int256[] memory assetDeltas);

    // Flash Loans

    /**
     * @dev Performs a 'flash loan', sending tokens to `recipient`, executing the `receiveFlashLoan` hook on it,
     * and then reverting unless the tokens plus a proportional protocol fee have been returned.
     *
     * The `tokens` and `amounts` arrays must have the same length, and each entry in these indicates the loan amount
     * for each token contract. `tokens` must be sorted in ascending order.
     *
     * The 'userData' field is ignored by the Vault, and forwarded as-is to `recipient` as part of the
     * `receiveFlashLoan` call.
     *
     * Emits `FlashLoan` events.
     */
    function flashLoan(
        IFlashLoanRecipient recipient,
        IERC20[] memory tokens,
        uint256[] memory amounts,
        bytes memory userData
    ) external;

    /**
     * @dev Emitted for each individual flash loan performed by `flashLoan`.
     */
    event FlashLoan(IFlashLoanRecipient indexed recipient, IERC20 indexed token, uint256 amount, uint256 feeAmount);

    // Asset Management
    //
    // Each token registered for a Pool can be assigned an Asset Manager, which is able to freely withdraw the Pool's
    // tokens from the Vault, deposit them, or assign arbitrary values to its `managed` balance (see
    // `getPoolTokenInfo`). This makes them extremely powerful and dangerous. Even if an Asset Manager only directly
    // controls one of the tokens in a Pool, a malicious manager could set that token's balance to manipulate the
    // prices of the other tokens, and then drain the Pool with swaps. The risk of using Asset Managers is therefore
    // not constrained to the tokens they are managing, but extends to the entire Pool's holdings.
    //
    // However, a properly designed Asset Manager smart contract can be safely used for the Pool's benefit,
    // for example by lending unused tokens out for interest, or using them to participate in voting protocols.
    //
    // This concept is unrelated to the IAsset interface.

    /**
     * @dev Performs a set of Pool balance operations, which may be either withdrawals, deposits or updates.
     *
     * Pool Balance management features batching, which means a single contract call can be used to perform multiple
     * operations of different kinds, with different Pools and tokens, at once.
     *
     * For each operation, the caller must be registered as the Asset Manager for `token` in `poolId`.
     */
    function managePoolBalance(PoolBalanceOp[] memory ops) external;

    struct PoolBalanceOp {
        PoolBalanceOpKind kind;
        bytes32 poolId;
        IERC20 token;
        uint256 amount;
    }

    /**
     * Withdrawals decrease the Pool's cash, but increase its managed balance, leaving the total balance unchanged.
     *
     * Deposits increase the Pool's cash, but decrease its managed balance, leaving the total balance unchanged.
     *
     * Updates don't affect the Pool's cash balance, but because the managed balance changes, it does alter the total.
     * The external amount can be either increased or decreased by this call (i.e., reporting a gain or a loss).
     */
    enum PoolBalanceOpKind { WITHDRAW, DEPOSIT, UPDATE }

    /**
     * @dev Emitted when a Pool's token Asset Manager alters its balance via `managePoolBalance`.
     */
    event PoolBalanceManaged(
        bytes32 indexed poolId,
        address indexed assetManager,
        IERC20 indexed token,
        int256 cashDelta,
        int256 managedDelta
    );

    // Protocol Fees
    //
    // Some operations cause the Vault to collect tokens in the form of protocol fees, which can then be withdrawn by
    // permissioned accounts.
    //
    // There are two kinds of protocol fees:
    //
    //  - flash loan fees: charged on all flash loans, as a percentage of the amounts lent.
    //
    //  - swap fees: a percentage of the fees charged by Pools when performing swaps. For a number of reasons, including
    // swap gas costs and interface simplicity, protocol swap fees are not charged on each individual swap. Rather,
    // Pools are expected to keep track of how much they have charged in swap fees, and pay any outstanding debts to the
    // Vault when they are joined or exited. This prevents users from joining a Pool with unpaid debt, as well as
    // exiting a Pool in debt without first paying their share.

    /**
     * @dev Returns the current protocol fee module.
     */
    function getProtocolFeesCollector() external view returns (ProtocolFeesCollector);

    /**
     * @dev Safety mechanism to pause most Vault operations in the event of an emergency - typically detection of an
     * error in some part of the system.
     *
     * The Vault can only be paused during an initial time period, after which pausing is forever disabled.
     *
     * While the contract is paused, the following features are disabled:
     * - depositing and transferring internal balance
     * - transferring external balance (using the Vault's allowance)
     * - swaps
     * - joining Pools
     * - Asset Manager interactions
     *
     * Internal Balance can still be withdrawn, and Pools exited.
     */
    function setPaused(bool paused) external;

    /**
     * @dev Returns the Vault's WETH instance.
     */
    function WETH() external view returns (IWETH);
    // solhint-disable-previous-line func-name-mixedcase
}

// File: contracts/balancer-core-v2/pools/BalancerPoolToken.sol



// SPDX-License-Identifier: GPL-3.0-or-later
// This program is free software: you can redistribute it and/or modify
// it under the terms of the GNU General Public License as published by
// the Free Software Foundation, either version 3 of the License, or
// (at your option) any later version.

// This program is distributed in the hope that it will be useful,
// but WITHOUT ANY WARRANTY; without even the implied warranty of
// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
// GNU General Public License for more details.

// You should have received a copy of the GNU General Public License
// along with this program.  If not, see <http://www.gnu.org/licenses/>.

pragma solidity ^0.7.0;

import "../lib/math/Math.sol";
import "../lib/openzeppelin/IERC20.sol";
import "../lib/openzeppelin/IERC20Permit.sol";
import "../lib/openzeppelin/EIP712.sol";

/**
 * @title Highly opinionated token implementation
 * @author Balancer Labs
 * @dev
 * - Includes functions to increase and decrease allowance as a workaround
 *   for the well-known issue with `approve`:
 *   https://github.com/ethereum/EIPs/issues/20#issuecomment-263524729
 * - Allows for 'infinite allowance', where an allowance of 0xff..ff is not
 *   decreased by calls to transferFrom
 * - Lets a token holder use `transferFrom` to send their own tokens,
 *   without first setting allowance
 * - Emits 'Approval' events whenever allowance is changed by `transferFrom`
 */
contract BalancerPoolToken is IERC20, IERC20Permit, EIP712 {
    using Math for uint256;

    // State variables

    uint8 private constant _DECIMALS = 18;

    mapping(address => uint256) private _balance;
    mapping(address => mapping(address => uint256)) private _allowance;
    uint256 private _totalSupply;

    string private _name;
    string private _symbol;

    mapping(address => uint256) private _nonces;

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

    // Function declarations

    constructor(string memory tokenName, string memory tokenSymbol) EIP712(tokenName, "1") {
        _name = tokenName;
        _symbol = tokenSymbol;
    }

    // External functions

    function allowance(address owner, address spender) external view override returns (uint256) {
        return _allowance[owner][spender];
    }

    function balanceOf(address account) external view override returns (uint256) {
        return _balance[account];
    }

    function approve(address spender, uint256 amount) external override returns (bool) {
        _setAllowance(msg.sender, spender, amount);

        return true;
    }

    function increaseApproval(address spender, uint256 amount) external returns (bool) {
        _setAllowance(msg.sender, spender, _allowance[msg.sender][spender].add(amount));

        return true;
    }

    function decreaseApproval(address spender, uint256 amount) external returns (bool) {
        uint256 currentAllowance = _allowance[msg.sender][spender];

        if (amount >= currentAllowance) {
            _setAllowance(msg.sender, spender, 0);
        } else {
            _setAllowance(msg.sender, spender, currentAllowance.sub(amount));
        }

        return true;
    }

    function transfer(address recipient, uint256 amount) external override returns (bool) {
        _move(msg.sender, recipient, amount);

        return true;
    }

    function transferFrom(
        address sender,
        address recipient,
        uint256 amount
    ) external override returns (bool) {
        uint256 currentAllowance = _allowance[sender][msg.sender];
        _require(msg.sender == sender || currentAllowance >= amount, Errors.INSUFFICIENT_ALLOWANCE);

        _move(sender, recipient, amount);

        if (msg.sender != sender && currentAllowance != uint256(-1)) {
            // Because of the previous require, we know that if msg.sender != sender then currentAllowance >= amount
            _setAllowance(sender, msg.sender, currentAllowance - amount);
        }

        return true;
    }

    function permit(
        address owner,
        address spender,
        uint256 value,
        uint256 deadline,
        uint8 v,
        bytes32 r,
        bytes32 s
    ) public virtual override {
        // solhint-disable-next-line not-rely-on-time
        _require(block.timestamp <= deadline, Errors.EXPIRED_PERMIT);

        uint256 nonce = _nonces[owner];

        bytes32 structHash = keccak256(abi.encode(_PERMIT_TYPE_HASH, owner, spender, value, nonce, deadline));

        bytes32 hash = _hashTypedDataV4(structHash);

        address signer = ecrecover(hash, v, r, s);
        _require((signer != address(0)) && (signer == owner), Errors.INVALID_SIGNATURE);

        _nonces[owner] = nonce + 1;
        _setAllowance(owner, spender, value);
    }

    // Public functions

    function name() public view returns (string memory) {
        return _name;
    }

    function symbol() public view returns (string memory) {
        return _symbol;
    }

    function decimals() public pure returns (uint8) {
        return _DECIMALS;
    }

    function totalSupply() public view override returns (uint256) {
        return _totalSupply;
    }

    function nonces(address owner) external view override returns (uint256) {
        return _nonces[owner];
    }

    // solhint-disable-next-line func-name-mixedcase
    function DOMAIN_SEPARATOR() external view override returns (bytes32) {
        return _domainSeparatorV4();
    }

    // Internal functions

    function _mintPoolTokens(address recipient, uint256 amount) internal {
        _balance[recipient] = _balance[recipient].add(amount);
        _totalSupply = _totalSupply.add(amount);
        emit Transfer(address(0), recipient, amount);
    }

    function _burnPoolTokens(address sender, uint256 amount) internal {
        uint256 currentBalance = _balance[sender];
        _require(currentBalance >= amount, Errors.INSUFFICIENT_BALANCE);

        _balance[sender] = currentBalance - amount;
        _totalSupply = _totalSupply.sub(amount);
        emit Transfer(sender, address(0), amount);
    }

    function _move(
        address sender,
        address recipient,
        uint256 amount
    ) internal {
        uint256 currentBalance = _balance[sender];
        _require(currentBalance >= amount, Errors.INSUFFICIENT_BALANCE);
        // Prohibit transfers to the zero address to avoid confusion with the
        // Transfer event emitted by `_burnPoolTokens`
        _require(recipient != address(0), Errors.ERC20_TRANSFER_TO_ZERO_ADDRESS);

        _balance[sender] = currentBalance - amount;
        _balance[recipient] = _balance[recipient].add(amount);

        emit Transfer(sender, recipient, amount);
    }

    // Private functions

    function _setAllowance(
        address owner,
        address spender,
        uint256 amount
    ) private {
        _allowance[owner][spender] = amount;
        emit Approval(owner, spender, amount);
    }
}

// File: contracts/balancer-core-v2/lib/openzeppelin/ERC20.sol



// SPDX-License-Identifier: MIT

pragma solidity ^0.7.0;

import "../helpers/BalancerErrors.sol";

import "./IERC20.sol";
import "./SafeMath.sol";

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

    mapping(address => uint256) private _balances;

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

    uint256 private _totalSupply;

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

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

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

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

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

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

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

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

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

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

    /**
     * @dev See {IERC20-transferFrom}.
     *
     * Emits an {Approval} event indicating the updated allowance. This is not
     * required by the EIP. See the note at the beginning of {ERC20}.
     *
     * Requirements:
     *
     * - `sender` and `recipient` cannot be the zero address.
     * - `sender` must have a balance of at least `amount`.
     * - the caller must have allowance for ``sender``'s tokens of at least
     * `amount`.
     */
    function transferFrom(
        address sender,
        address recipient,
        uint256 amount
    ) public virtual override returns (bool) {
        _transfer(sender, recipient, amount);
        _approve(
            sender,
            msg.sender,
            _allowances[sender][msg.sender].sub(amount, Errors.ERC20_TRANSFER_EXCEEDS_ALLOWANCE)
        );
        return true;
    }

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

    /**
     * @dev Atomically decreases the allowance granted to `spender` by the caller.
     *
     * This is an alternative to {approve} that can be used as a mitigation for
     * problems described in {IERC20-approve}.
     *
     * Emits an {Approval} event indicating the updated allowance.
     *
     * Requirements:
     *
     * - `spender` cannot be the zero address.
     * - `spender` must have allowance for the caller of at least
     * `subtractedValue`.
     */
    function decreaseAllowance(address spender, uint256 subtractedValue) public virtual returns (bool) {
        _approve(
            msg.sender,
            spender,
            _allowances[msg.sender][spender].sub(subtractedValue, Errors.ERC20_DECREASED_ALLOWANCE_BELOW_ZERO)
        );
        return true;
    }

    /**
     * @dev Moves tokens `amount` from `sender` to `recipient`.
     *
     * This is internal function is equivalent to {transfer}, and can be used to
     * e.g. implement automatic token fees, slashing mechanisms, etc.
     *
     * Emits a {Transfer} event.
     *
     * Requirements:
     *
     * - `sender` cannot be the zero address.
     * - `recipient` cannot be the zero address.
     * - `sender` must have a balance of at least `amount`.
     */
    function _transfer(
        address sender,
        address recipient,
        uint256 amount
    ) internal virtual {
        _require(sender != address(0), Errors.ERC20_TRANSFER_FROM_ZERO_ADDRESS);
        _require(recipient != address(0), Errors.ERC20_TRANSFER_TO_ZERO_ADDRESS);

        _beforeTokenTransfer(sender, recipient, amount);

        _balances[sender] = _balances[sender].sub(amount, Errors.ERC20_TRANSFER_EXCEEDS_BALANCE);
        _balances[recipient] = _balances[recipient].add(amount);
        emit Transfer(sender, recipient, amount);
    }

    /** @dev Creates `amount` tokens and assigns them to `account`, increasing
     * the total supply.
     *
     * Emits a {Transfer} event with `from` set to the zero address.
     *
     * Requirements:
     *
     * - `to` cannot be the zero address.
     */
    function _mint(address account, uint256 amount) internal virtual {
        _require(account != address(0), Errors.ERC20_MINT_TO_ZERO_ADDRESS);

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

        _totalSupply = _totalSupply.add(amount);
        _balances[account] = _balances[account].add(amount);
        emit Transfer(address(0), account, amount);
    }

    /**
     * @dev Destroys `amount` tokens from `account`, reducing the
     * total supply.
     *
     * Emits a {Transfer} event with `to` set to the zero address.
     *
     * Requirements:
     *
     * - `account` cannot be the zero address.
     * - `account` must have at least `amount` tokens.
     */
    function _burn(address account, uint256 amount) internal virtual {
        _require(account != address(0), Errors.ERC20_BURN_FROM_ZERO_ADDRESS);

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

        _balances[account] = _balances[account].sub(amount, Errors.ERC20_BURN_EXCEEDS_ALLOWANCE);
        _totalSupply = _totalSupply.sub(amount);
        emit Transfer(account, address(0), amount);
    }

    /**
     * @dev Sets `amount` as the allowance of `spender` over the `owner` s tokens.
     *
     * This internal function is equivalent to `approve`, and can be used to
     * e.g. set automatic allowances for certain subsystems, etc.
     *
     * Emits an {Approval} event.
     *
     * Requirements:
     *
     * - `owner` cannot be the zero address.
     * - `spender` cannot be the zero address.
     */
    function _approve(
        address owner,
        address spender,
        uint256 amount
    ) internal virtual {
        _require(owner != address(0), Errors.ERC20_APPROVE_FROM_ZERO_ADDRESS);
        _require(spender != address(0), Errors.ERC20_APPROVE_TO_ZERO_ADDRESS);

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

    /**
     * @dev Sets {decimals} to a value other than the default one of 18.
     *
     * WARNING: This function should only be called from the constructor. Most
     * applications that interact with token contracts will not expect
     * {decimals} to ever change, and may work incorrectly if it does.
     */
    function _setupDecimals(uint8 decimals_) internal {
        _decimals = decimals_;
    }

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

// File: contracts/balancer-core-v2/lib/helpers/BalancerErrors.sol



// SPDX-License-Identifier: GPL-3.0-or-later
// This program is free software: you can redistribute it and/or modify
// it under the terms of the GNU General Public License as published by
// the Free Software Foundation, either version 3 of the License, or
// (at your option) any later version.

// This program is distributed in the hope that it will be useful,
// but WITHOUT ANY WARRANTY; without even the implied warranty of
// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
// GNU General Public License for more details.

// You should have received a copy of the GNU General Public License
// along with this program.  If not, see <http://www.gnu.org/licenses/>.

pragma solidity ^0.7.0;

// solhint-disable

/**
 * @dev Reverts if `condition` is false, with a revert reason containing `errorCode`. Only codes up to 999 are
 * supported.
 */
function _require(bool condition, uint256 errorCode) pure {
    if (!condition) _revert(errorCode);
}

/**
 * @dev Reverts with a revert reason containing `errorCode`. Only codes up to 999 are supported.
 */
function _revert(uint256 errorCode) pure {
    // We're going to dynamically create a revert string based on the error code, with the following format:
    // 'BAL#{errorCode}'
    // where the code is left-padded with zeroes to three digits (so they range from 000 to 999).
    //
    // We don't have revert strings embedded in the contract to save bytecode size: it takes much less space to store a
    // number (8 to 16 bits) than the individual string characters.
    //
    // The dynamic string creation algorithm that follows could be implemented in Solidity, but assembly allows for a
    // much denser implementation, again saving bytecode size. Given this function unconditionally reverts, this is a
    // safe place to rely on it without worrying about how its usage might affect e.g. memory contents.
    assembly {
        // First, we need to compute the ASCII representation of the error code. We assume that it is in the 0-999
        // range, so we only need to convert three digits. To convert the digits to ASCII, we add 0x30, the value for
        // the '0' character.

        let units := add(mod(errorCode, 10), 0x30)

        errorCode := div(errorCode, 10)
        let tenths := add(mod(errorCode, 10), 0x30)

        errorCode := div(errorCode, 10)
        let hundreds := add(mod(errorCode, 10), 0x30)

        // With the individual characters, we can now construct the full string. The "BAL#" part is a known constant
        // (0x42414c23): we simply shift this by 24 (to provide space for the 3 bytes of the error code), and add the
        // characters to it, each shifted by a multiple of 8.
        // The revert reason is then shifted left by 200 bits (256 minus the length of the string, 7 characters * 8 bits
        // per character = 56) to locate it in the most significant part of the 256 slot (the beginning of a byte
        // array).

        let revertReason := shl(200, add(0x42414c23000000, add(add(units, shl(8, tenths)), shl(16, hundreds))))

        // We can now encode the reason in memory, which can be safely overwritten as we're about to revert. The encoded
        // message will have the following layout:
        // [ revert reason identifier ] [ string location offset ] [ string length ] [ string contents ]

        // The Solidity revert reason identifier is 0x08c739a0, the function selector of the Error(string) function. We
        // also write zeroes to the next 28 bytes of memory, but those are about to be overwritten.
        mstore(0x0, 0x08c379a000000000000000000000000000000000000000000000000000000000)
        // Next is the offset to the location of the string, which will be placed immediately after (20 bytes away).
        mstore(0x04, 0x0000000000000000000000000000000000000000000000000000000000000020)
        // The string length is fixed: 7 characters.
        mstore(0x24, 7)
        // Finally, the string itself is stored.
        mstore(0x44, revertReason)

        // Even if the string is only 7 bytes long, we need to return a full 32 byte slot containing it. The length of
        // the encoded message is therefore 4 + 32 + 32 + 32 = 100.
        revert(0, 100)
    }
}

library Errors {
    // Math
    uint256 internal constant ADD_OVERFLOW = 0;
    uint256 internal constant SUB_OVERFLOW = 1;
    uint256 internal constant SUB_UNDERFLOW = 2;
    uint256 internal constant MUL_OVERFLOW = 3;
    uint256 internal constant ZERO_DIVISION = 4;
    uint256 internal constant DIV_INTERNAL = 5;
    uint256 internal constant X_OUT_OF_BOUNDS = 6;
    uint256 internal constant Y_OUT_OF_BOUNDS = 7;
    uint256 internal constant PRODUCT_OUT_OF_BOUNDS = 8;
    uint256 internal constant INVALID_EXPONENT = 9;

    // Input
    uint256 internal constant OUT_OF_BOUNDS = 100;
    uint256 internal constant UNSORTED_ARRAY = 101;
    uint256 internal constant UNSORTED_TOKENS = 102;
    uint256 internal constant INPUT_LENGTH_MISMATCH = 103;
    uint256 internal constant ZERO_TOKEN = 104;

    // Shared pools
    uint256 internal constant MIN_TOKENS = 200;
    uint256 internal constant MAX_TOKENS = 201;
    uint256 internal constant MAX_SWAP_FEE_PERCENTAGE = 202;
    uint256 internal constant MIN_SWAP_FEE_PERCENTAGE = 203;
    uint256 internal constant MINIMUM_BPT = 204;
    uint256 internal constant CALLER_NOT_VAULT = 205;
    uint256 internal constant UNINITIALIZED = 206;
    uint256 internal constant BPT_IN_MAX_AMOUNT = 207;
    uint256 internal constant BPT_OUT_MIN_AMOUNT = 208;
    uint256 internal constant EXPIRED_PERMIT = 209;

    // Pools
    uint256 internal constant MIN_AMP = 300;
    uint256 internal constant MAX_AMP = 301;
    uint256 internal constant MIN_WEIGHT = 302;
    uint256 internal constant MAX_STABLE_TOKENS = 303;
    uint256 internal constant MAX_IN_RATIO = 304;
    uint256 internal constant MAX_OUT_RATIO = 305;
    uint256 internal constant MIN_BPT_IN_FOR_TOKEN_OUT = 306;
    uint256 internal constant MAX_OUT_BPT_FOR_TOKEN_IN = 307;
    uint256 internal constant NORMALIZED_WEIGHT_INVARIANT = 308;
    uint256 internal constant INVALID_TOKEN = 309;
    uint256 internal constant UNHANDLED_JOIN_KIND = 310;
    uint256 internal constant ZERO_INVARIANT = 311;
    uint256 internal constant ORACLE_INVALID_SECONDS_QUERY = 312;
    uint256 internal constant ORACLE_NOT_INITIALIZED = 313;
    uint256 internal constant ORACLE_QUERY_TOO_OLD = 314;
    uint256 internal constant ORACLE_INVALID_INDEX = 315;
    uint256 internal constant ORACLE_BAD_SECS = 316;

    // Lib
    uint256 internal constant REENTRANCY = 400;
    uint256 internal constant SENDER_NOT_ALLOWED = 401;
    uint256 internal constant PAUSED = 402;
    uint256 internal constant PAUSE_WINDOW_EXPIRED = 403;
    uint256 internal constant MAX_PAUSE_WINDOW_DURATION = 404;
    uint256 internal constant MAX_BUFFER_PERIOD_DURATION = 405;
    uint256 internal constant INSUFFICIENT_BALANCE = 406;
    uint256 internal constant INSUFFICIENT_ALLOWANCE = 407;
    uint256 internal constant ERC20_TRANSFER_FROM_ZERO_ADDRESS = 408;
    uint256 internal constant ERC20_TRANSFER_TO_ZERO_ADDRESS = 409;
    uint256 internal constant ERC20_MINT_TO_ZERO_ADDRESS = 410;
    uint256 internal constant ERC20_BURN_FROM_ZERO_ADDRESS = 411;
    uint256 internal constant ERC20_APPROVE_FROM_ZERO_ADDRESS = 412;
    uint256 internal constant ERC20_APPROVE_TO_ZERO_ADDRESS = 413;
    uint256 internal constant ERC20_TRANSFER_EXCEEDS_ALLOWANCE = 414;
    uint256 internal constant ERC20_DECREASED_ALLOWANCE_BELOW_ZERO = 415;
    uint256 internal constant ERC20_TRANSFER_EXCEEDS_BALANCE = 416;
    uint256 internal constant ERC20_BURN_EXCEEDS_ALLOWANCE = 417;
    uint256 internal constant SAFE_ERC20_CALL_FAILED = 418;
    uint256 internal constant ADDRESS_INSUFFICIENT_BALANCE = 419;
    uint256 internal constant ADDRESS_CANNOT_SEND_VALUE = 420;
    uint256 internal constant SAFE_CAST_VALUE_CANT_FIT_INT256 = 421;
    uint256 internal constant GRANT_SENDER_NOT_ADMIN = 422;
    uint256 internal constant REVOKE_SENDER_NOT_ADMIN = 423;
    uint256 internal constant RENOUNCE_SENDER_NOT_ALLOWED = 424;
    uint256 internal constant BUFFER_PERIOD_EXPIRED = 425;

    // Vault
    uint256 internal constant INVALID_POOL_ID = 500;
    uint256 internal constant CALLER_NOT_POOL = 501;
    uint256 internal constant SENDER_NOT_ASSET_MANAGER = 502;
    uint256 internal constant USER_DOESNT_ALLOW_RELAYER = 503;
    uint256 internal constant INVALID_SIGNATURE = 504;
    uint256 internal constant EXIT_BELOW_MIN = 505;
    uint256 internal constant JOIN_ABOVE_MAX = 506;
    uint256 internal constant SWAP_LIMIT = 507;
    uint256 internal constant SWAP_DEADLINE = 508;
    uint256 internal constant CANNOT_SWAP_SAME_TOKEN = 509;
    uint256 internal constant UNKNOWN_AMOUNT_IN_FIRST_SWAP = 510;
    uint256 internal constant MALCONSTRUCTED_MULTIHOP_SWAP = 511;
    uint256 internal constant INTERNAL_BALANCE_OVERFLOW = 512;
    uint256 internal constant INSUFFICIENT_INTERNAL_BALANCE = 513;
    uint256 internal constant INVALID_ETH_INTERNAL_BALANCE = 514;
    uint256 internal constant INVALID_POST_LOAN_BALANCE = 515;
    uint256 internal constant INSUFFICIENT_ETH = 516;
    uint256 internal constant UNALLOCATED_ETH = 517;
    uint256 internal constant ETH_TRANSFER = 518;
    uint256 internal constant CANNOT_USE_ETH_SENTINEL = 519;
    uint256 internal constant TOKENS_MISMATCH = 520;
    uint256 internal constant TOKEN_NOT_REGISTERED = 521;
    uint256 internal constant TOKEN_ALREADY_REGISTERED = 522;
    uint256 internal constant TOKENS_ALREADY_SET = 523;
    uint256 internal constant TOKENS_LENGTH_MUST_BE_2 = 524;
    uint256 internal constant NONZERO_TOKEN_BALANCE = 525;
    uint256 internal constant BALANCE_TOTAL_OVERFLOW = 526;
    uint256 internal constant POOL_NO_TOKENS = 527;
    uint256 internal constant INSUFFICIENT_FLASH_LOAN_BALANCE = 528;

    // Fees
    uint256 internal constant SWAP_FEE_PERCENTAGE_TOO_HIGH = 600;
    uint256 internal constant FLASH_LOAN_FEE_PERCENTAGE_TOO_HIGH = 601;
    uint256 internal constant INSUFFICIENT_FLASH_LOAN_FEE_AMOUNT = 602;
}

// File: contracts/balancer-core-v2/lib/openzeppelin/IERC20.sol



// SPDX-License-Identifier: MIT

pragma solidity ^0.7.0;

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

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

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

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

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

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

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

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

// File: contracts/balancer-core-v2/lib/openzeppelin/SafeMath.sol



// SPDX-License-Identifier: MIT

pragma solidity ^0.7.0;

import "../helpers/BalancerErrors.sol";

/**
 * @dev Wrappers over Solidity's arithmetic operations with added overflow
 * checks.
 *
 * Arithmetic operations in Solidity wrap on overflow. This can easily result
 * in bugs, because programmers usually assume that an overflow raises an
 * error, which is the standard behavior in high level programming languages.
 * `SafeMath` restores this intuition by reverting the transaction when an
 * operation overflows.
 *
 * Using this library instead of the unchecked operations eliminates an entire
 * class of bugs, so it's recommended to use it always.
 */
library SafeMath {
    /**
     * @dev Returns the addition of two unsigned integers, reverting on
     * overflow.
     *
     * Counterpart to Solidity's `+` operator.
     *
     * Requirements:
     *
     * - Addition cannot overflow.
     */
    function add(uint256 a, uint256 b) internal pure returns (uint256) {
        uint256 c = a + b;
        _require(c >= a, Errors.ADD_OVERFLOW);

        return c;
    }

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

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

        return c;
    }
}

// File: contracts/balancer-core-v2/vault/interfaces/IBasePool.sol



// SPDX-License-Identifier: GPL-3.0-or-later
// This program is free software: you can redistribute it and/or modify
// it under the terms of the GNU General Public License as published by
// the Free Software Foundation, either version 3 of the License, or
// (at your option) any later version.

// This program is distributed in the hope that it will be useful,
// but WITHOUT ANY WARRANTY; without even the implied warranty of
// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
// GNU General Public License for more details.

// You should have received a copy of the GNU General Public License
// along with this program.  If not, see <http://www.gnu.org/licenses/>.

pragma solidity ^0.7.0;
pragma experimental ABIEncoderV2;

import "./IVault.sol";
import "./IPoolSwapStructs.sol";

/**
 * @dev Interface for adding and removing liquidity that all Pool contracts should implement. Note that this is not
 * the complete Pool contract interface, as it is missing the swap hooks. Pool contracts should also inherit from
 * either IGeneralPool or IMinimalSwapInfoPool
 */
interface IBasePool is IPoolSwapStructs {
    /**
     * @dev Called by the Vault when a user calls `IVault.joinPool` to add liquidity to this Pool. Returns how many of
     * each registered token the user should provide, as well as the amount of protocol fees the Pool owes to the Vault.
     * The Vault will then take tokens from `sender` and add them to the Pool's balances, as well as collect
     * the reported amount in protocol fees, which the pool should calculate based on `protocolSwapFeePercentage`.
     *
     * Protocol fees are reported and charged on join events so that the Pool is free of debt whenever new users join.
     *
     * `sender` is the account performing the join (from which tokens will be withdrawn), and `recipient` is the account
     * designated to receive any benefits (typically pool shares). `currentBalances` contains the total balances
     * for each token the Pool registered in the Vault, in the same order that `IVault.getPoolTokens` would return.
     *
     * `lastChangeBlock` is the last block in which *any* of the Pool's registered tokens last changed its total
     * balance.
     *
     * `userData` contains any pool-specific instructions needed to perform the calculations, such as the type of
     * join (e.g., proportional given an amount of pool shares, single-asset, multi-asset, etc.)
     *
     * Contracts implementing this function should check that the caller is indeed the Vault before performing any
     * state-changing operations, such as minting pool shares.
     */
    function onJoinPool(
        bytes32 poolId,
        address sender,
        address recipient,
        uint256[] memory balances,
        uint256 lastChangeBlock,
        uint256 protocolSwapFeePercentage,
        bytes memory userData
    ) external returns (uint256[] memory amountsIn, uint256[] memory dueProtocolFeeAmounts);

    /**
     * @dev Called by the Vault when a user calls `IVault.exitPool` to remove liquidity from this Pool. Returns how many
     * tokens the Vault should deduct from the Pool's balances, as well as the amount of protocol fees the Pool owes
     * to the Vault. The Vault will then take tokens from the Pool's balances and send them to `recipient`,
     * as well as collect the reported amount in protocol fees, which the Pool should calculate based on
     * `protocolSwapFeePercentage`.
     *
     * Protocol fees are charged on exit events to guarantee that users exiting the Pool have paid their share.
     *
     * `sender` is the account performing the exit (typically the pool shareholder), and `recipient` is the account
     * to which the Vault will send the proceeds. `currentBalances` contains the total token balances for each token
     * the Pool registered in the Vault, in the same order that `IVault.getPoolTokens` would return.
     *
     * `lastChangeBlock` is the last block in which *any* of the Pool's registered tokens last changed its total
     * balance.
     *
     * `userData` contains any pool-specific instructions needed to perform the calculations, such as the type of
     * exit (e.g., proportional given an amount of pool shares, single-asset, multi-asset, etc.)
     *
     * Contracts implementing this function should check that the caller is indeed the Vault before performing any
     * state-changing operations, such as burning pool shares.
     */
    function onExitPool(
        bytes32 poolId,
        address sender,
        address recipient,
        uint256[] memory balances,
        uint256 lastChangeBlock,
        uint256 protocolSwapFeePercentage,
        bytes memory userData
    ) external returns (uint256[] memory amountsOut, uint256[] memory dueProtocolFeeAmounts);
}

// File: contracts/balancer-core-v2/vault/interfaces/IPoolSwapStructs.sol



// SPDX-License-Identifier: GPL-3.0-or-later
// This program is free software: you can redistribute it and/or modify
// it under the terms of the GNU General Public License as published by
// the Free Software Foundation, either version 3 of the License, or
// (at your option) any later version.

// This program is distributed in the hope that it will be useful,
// but WITHOUT ANY WARRANTY; without even the implied warranty of
// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
// GNU General Public License for more details.

// You should have received a copy of the GNU General Public License
// along with this program.  If not, see <http://www.gnu.org/licenses/>.

pragma solidity ^0.7.0;
pragma experimental ABIEncoderV2;

import "../../lib/openzeppelin/IERC20.sol";

import "./IVault.sol";

interface IPoolSwapStructs {
    // This is not really an interface - it just defines common structs used by other interfaces: IGeneralPool and
    // IMinimalSwapInfoPool.
    //
    // This data structure represents a request for a token swap, where `kind` indicates the swap type ('given in' or
    // 'given out') which indicates whether or not the amount sent by the pool is known.
    //
    // The pool receives `tokenIn` and sends `tokenOut`. `amount` is the number of `tokenIn` tokens the pool will take
    // in, or the number of `tokenOut` tokens the Pool will send out, depending on the given swap `kind`.
    //
    // All other fields are not strictly necessary for most swaps, but are provided to support advanced scenarios in
    // some Pools.
    //
    // `poolId` is the ID of the Pool involved in the swap - this is useful for Pool contracts that implement more than
    // one Pool.
    //
    // The meaning of `lastChangeBlock` depends on the Pool specialization:
    //  - Two Token or Minimal Swap Info: the last block in which either `tokenIn` or `tokenOut` changed its total
    //    balance.
    //  - General: the last block in which *any* of the Pool's registered tokens changed its total balance.
    //
    // `from` is the origin address for the funds the Pool receives, and `to` is the destination address
    // where the Pool sends the outgoing tokens.
    //
    // `userData` is extra data provided by the caller - typically a signature from a trusted party.
    struct SwapRequest {
        IVault.SwapKind kind;
        IERC20 tokenIn;
        IERC20 tokenOut;
        uint256 amount;
        // Misc data
        bytes32 poolId;
        uint256 lastChangeBlock;
        address from;
        address to;
        bytes userData;
    }
}

// File: contracts/balancer-core-v2/vault/interfaces/IWETH.sol



// SPDX-License-Identifier: GPL-3.0-or-later
// This program is free software: you can redistribute it and/or modify
// it under the terms of the GNU General Public License as published by
// the Free Software Foundation, either version 3 of the License, or
// (at your option) any later version.

// This program is distributed in the hope that it will be useful,
// but WITHOUT ANY WARRANTY; without even the implied warranty of
// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
// GNU General Public License for more details.

// You should have received a copy of the GNU General Public License
// along with this program.  If not, see <http://www.gnu.org/licenses/>.

pragma solidity ^0.7.0;

import "../../lib/openzeppelin/IERC20.sol";

/**
 * @dev Interface for the WETH token contract used internally for wrapping and unwrapping, to support
 * sending and receiving ETH in joins, swaps, and internal balance deposits and withdrawals.
 */
interface IWETH is IERC20 {
    function deposit() external payable;

    function withdraw(uint256 amount) external;
}

// File: contracts/balancer-core-v2/vault/interfaces/IAsset.sol



// SPDX-License-Identifier: GPL-3.0-or-later
// This program is free software: you can redistribute it and/or modify
// it under the terms of the GNU General Public License as published by
// the Free Software Foundation, either version 3 of the License, or
// (at your option) any later version.

// This program is distributed in the hope that it will be useful,
// but WITHOUT ANY WARRANTY; without even the implied warranty of
// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
// GNU General Public License for more details.

// You should have received a copy of the GNU General Public License
// along with this program.  If not, see <http://www.gnu.org/licenses/>.

pragma solidity ^0.7.0;

/**
 * @dev This is an empty interface used to represent either ERC20-conforming token contracts or ETH (using the zero
 * address sentinel value). We're just relying on the fact that `interface` can be used to declare new address-like
 * types.
 *
 * This concept is unrelated to a Pool's Asset Managers.
 */
interface IAsset {
    // solhint-disable-previous-line no-empty-blocks
}

// File: contracts/balancer-core-v2/vault/interfaces/IAuthorizer.sol



// SPDX-License-Identifier: GPL-3.0-or-later
// This program is free software: you can redistribute it and/or modify
// it under the terms of the GNU General Public License as published by
// the Free Software Foundation, either version 3 of the License, or
// (at your option) any later version.

// This program is distributed in the hope that it will be useful,
// but WITHOUT ANY WARRANTY; without even the implied warranty of
// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
// GNU General Public License for more details.

// You should have received a copy of the GNU General Public License
// along with this program.  If not, see <http://www.gnu.org/licenses/>.

pragma solidity ^0.7.0;

interface IAuthorizer {
    /**
     * @dev Returns true if `account` can perform the action described by `actionId` in the contract `where`.
     */
    function canPerform(
        bytes32 actionId,
        address account,
        address where
    ) external view returns (bool);
}

// File: contracts/balancer-core-v2/vault/interfaces/IFlashLoanRecipient.sol



// SPDX-License-Identifier: GPL-3.0-or-later
// This program is free software: you can redistribute it and/or modify
// it under the terms of the GNU General Public License as published by
// the Free Software Foundation, either version 3 of the License, or
// (at your option) any later version.

// This program is distributed in the hope that it will be useful,
// but WITHOUT ANY WARRANTY; without even the implied warranty of
// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
// GNU General Public License for more details.

// You should have received a copy of the GNU General Public License
// along with this program.  If not, see <http://www.gnu.org/licenses/>.

pragma solidity ^0.7.0;

// Inspired by Aave Protocol's IFlashLoanReceiver.

import "../../lib/openzeppelin/IERC20.sol";

interface IFlashLoanRecipient {
    /**
     * @dev When `flashLoan` is called on the Vault, it invokes the `receiveFlashLoan` hook on the recipient.
     *
     * At the time of the call, the Vault will have transferred `amounts` for `tokens` to the recipient. Before this
     * call returns, the recipient must have transferred `amounts` plus `feeAmounts` for each token back to the
     * Vault, or else the entire flash loan will revert.
     *
     * `userData` is the same value passed in the `IVault.flashLoan` call.
     */
    function receiveFlashLoan(
        IERC20[] memory tokens,
        uint256[] memory amounts,
        uint256[] memory feeAmounts,
        bytes memory userData
    ) external;
}

// File: contracts/balancer-core-v2/vault/ProtocolFeesCollector.sol



// SPDX-License-Identifier: GPL-3.0-or-later
// This program is free software: you can redistribute it and/or modify
// it under the terms of the GNU General Public License as published by
// the Free Software Foundation, either version 3 of the License, or
// (at your option) any later version.

// This program is distributed in the hope that it will be useful,
// but WITHOUT ANY WARRANTY; without even the implied warranty of
// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
// GNU General Public License for more details.

// You should have received a copy of the GNU General Public License
// along with this program.  If not, see <http://www.gnu.org/licenses/>.

pragma solidity ^0.7.0;
pragma experimental ABIEncoderV2;

import "../lib/openzeppelin/IERC20.sol";
import "../lib/helpers/InputHelpers.sol";
import "../lib/helpers/Authentication.sol";
import "../lib/openzeppelin/ReentrancyGuard.sol";
import "../lib/openzeppelin/SafeERC20.sol";

import "./interfaces/IVault.sol";
import "./interfaces/IAuthorizer.sol";

/**
 * @dev This an auxiliary contract to the Vault, deployed by it during construction. It offloads some of the tasks the
 * Vault performs to reduce its overall bytecode size.
 *
 * The current values for all protocol fee percentages are stored here, and any tokens charged as protocol fees are
 * sent to this contract, where they may be withdrawn by authorized entities. All authorization tasks are delegated
 * to the Vault's own authorizer.
 */
contract ProtocolFeesCollector is Authentication, ReentrancyGuard {
    using SafeERC20 for IERC20;

    // Absolute maximum fee percentages (1e18 = 100%, 1e16 = 1%).
    uint256 private constant _MAX_PROTOCOL_SWAP_FEE_PERCENTAGE = 50e16; // 50%
    uint256 private constant _MAX_PROTOCOL_FLASH_LOAN_FEE_PERCENTAGE = 1e16; // 1%

    IVault public immutable vault;

    // All fee percentages are 18-decimal fixed point numbers.

    // The swap fee is charged whenever a swap occurs, as a percentage of the fee charged by the Pool. These are not
    // actually charged on each individual swap: the `Vault` relies on the Pools being honest and reporting fees due
    // when users join and exit them.
    uint256 private _swapFeePercentage;

    // The flash loan fee is charged whenever a flash loan occurs, as a percentage of the tokens lent.
    uint256 private _flashLoanFeePercentage;

    event SwapFeePercentageChanged(uint256 newSwapFeePercentage);
    event FlashLoanFeePercentageChanged(uint256 newFlashLoanFeePercentage);

    constructor(IVault _vault)
        // The ProtocolFeesCollector is a singleton, so it simply uses its own address to disambiguate action
        // identifiers.
        Authentication(bytes32(uint256(address(this))))
    {
        vault = _vault;
    }

    function withdrawCollectedFees(
        IERC20[] calldata tokens,
        uint256[] calldata amounts,
        address recipient
    ) external nonReentrant authenticate {
        InputHelpers.ensureInputLengthMatch(tokens.length, amounts.length);

        for (uint256 i = 0; i < tokens.length; ++i) {
            IERC20 token = tokens[i];
            uint256 amount = amounts[i];
            token.safeTransfer(recipient, amount);
        }
    }

    function setSwapFeePercentage(uint256 newSwapFeePercentage) external authenticate {
        _require(newSwapFeePercentage <= _MAX_PROTOCOL_SWAP_FEE_PERCENTAGE, Errors.SWAP_FEE_PERCENTAGE_TOO_HIGH);
        _swapFeePercentage = newSwapFeePercentage;
        emit SwapFeePercentageChanged(newSwapFeePercentage);
    }

    function setFlashLoanFeePercentage(uint256 newFlashLoanFeePercentage) external authenticate {
        _require(
            newFlashLoanFeePercentage <= _MAX_PROTOCOL_FLASH_LOAN_FEE_PERCENTAGE,
            Errors.FLASH_LOAN_FEE_PERCENTAGE_TOO_HIGH
        );
        _flashLoanFeePercentage = newFlashLoanFeePercentage;
        emit FlashLoanFeePercentageChanged(newFlashLoanFeePercentage);
    }

    function getSwapFeePercentage() external view returns (uint256) {
        return _swapFeePercentage;
    }

    function getFlashLoanFeePercentage() external view returns (uint256) {
        return _flashLoanFeePercentage;
    }

    function getCollectedFeeAmounts(IERC20[] memory tokens) external view returns (uint256[] memory feeAmounts) {
        feeAmounts = new uint256[](tokens.length);
        for (uint256 i = 0; i < tokens.length; ++i) {
            feeAmounts[i] = tokens[i].balanceOf(address(this));
        }
    }

    function getAuthorizer() external view returns (IAuthorizer) {
        return _getAuthorizer();
    }

    function _canPerform(bytes32 actionId, address account) internal view override returns (bool) {
        return _getAuthorizer().canPerform(actionId, account, address(this));
    }

    function _getAuthorizer() internal view returns (IAuthorizer) {
        return vault.getAuthorizer();
    }
}

// File: contracts/balancer-core-v2/lib/helpers/ISignaturesValidator.sol



// SPDX-License-Identifier: GPL-3.0-or-later
// This program is free software: you can redistribute it and/or modify
// it under the terms of the GNU General Public License as published by
// the Free Software Foundation, either version 3 of the License, or
// (at your option) any later version.

// This program is distributed in the hope that it will be useful,
// but WITHOUT ANY WARRANTY; without even the implied warranty of
// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
// GNU General Public License for more details.

// You should have received a copy of the GNU General Public License
// along with this program.  If not, see <http://www.gnu.org/licenses/>.

pragma solidity ^0.7.0;

/**
 * @dev Interface for the SignatureValidator helper, used to support meta-transactions.
 */
interface ISignaturesValidator {
    /**
     * @dev Returns the EIP712 domain separator.
     */
    function getDomainSeparator() external view returns (bytes32);

    /**
     * @dev Returns the next nonce used by an address to sign messages.
     */
    function getNextNonce(address user) external view returns (uint256);
}

// File: contracts/balancer-core-v2/lib/helpers/ITemporarilyPausable.sol



// SPDX-License-Identifier: GPL-3.0-or-later
// This program is free software: you can redistribute it and/or modify
// it under the terms of the GNU General Public License as published by
// the Free Software Foundation, either version 3 of the License, or
// (at your option) any later version.

// This program is distributed in the hope that it will be useful,
// but WITHOUT ANY WARRANTY; without even the implied warranty of
// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
// GNU General Public License for more details.

// You should have received a copy of the GNU General Public License
// along with this program.  If not, see <http://www.gnu.org/licenses/>.

pragma solidity ^0.7.0;

/**
 * @dev Interface for the TemporarilyPausable helper.
 */
interface ITemporarilyPausable {
    /**
     * @dev Emitted every time the pause state changes by `_setPaused`.
     */
    event PausedStateChanged(bool paused);

    /**
     * @dev Returns the current paused state.
     */
    function getPausedState()
        external
        view
        returns (
            bool paused,
            uint256 pauseWindowEndTime,
            uint256 bufferPeriodEndTime
        );
}

// File: contracts/balancer-core-v2/lib/helpers/InputHelpers.sol



// SPDX-License-Identifier: GPL-3.0-or-later
// This program is free software: you can redistribute it and/or modify
// it under the terms of the GNU General Public License as published by
// the Free Software Foundation, either version 3 of the License, or
// (at your option) any later version.

// This program is distributed in the hope that it will be useful,
// but WITHOUT ANY WARRANTY; without even the implied warranty of
// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
// GNU General Public License for more details.

// You should have received a copy of the GNU General Public License
// along with this program.  If not, see <http://www.gnu.org/licenses/>.

pragma solidity ^0.7.0;

import "../openzeppelin/IERC20.sol";

import "./BalancerErrors.sol";

import "../../vault/interfaces/IAsset.sol";

library InputHelpers {
    function ensureInputLengthMatch(uint256 a, uint256 b) internal pure {
        _require(a == b, Errors.INPUT_LENGTH_MISMATCH);
    }

    function ensureInputLengthMatch(
        uint256 a,
        uint256 b,
        uint256 c
    ) internal pure {
        _require(a == b && b == c, Errors.INPUT_LENGTH_MISMATCH);
    }

    function ensureArrayIsSorted(IAsset[] memory array) internal pure {
        address[] memory addressArray;
        // solhint-disable-next-line no-inline-assembly
        assembly {
            addressArray := array
        }
        ensureArrayIsSorted(addressArray);
    }

    function ensureArrayIsSorted(IERC20[] memory array) internal pure {
        address[] memory addressArray;
        // solhint-disable-next-line no-inline-assembly
        assembly {
            addressArray := array
        }
        ensureArrayIsSorted(addressArray);
    }

    function ensureArrayIsSorted(address[] memory array) internal pure {
        if (array.length < 2) {
            return;
        }

        address previous = array[0];
        for (uint256 i = 1; i < array.length; ++i) {
            address current = array[i];
            _require(previous < current, Errors.UNSORTED_ARRAY);
            previous = current;
        }
    }
}

// File: contracts/balancer-core-v2/lib/helpers/Authentication.sol



// SPDX-License-Identifier: GPL-3.0-or-later
// This program is free software: you can redistribute it and/or modify
// it under the terms of the GNU General Public License as published by
// the Free Software Foundation, either version 3 of the License, or
// (at your option) any later version.

// This program is distributed in the hope that it will be useful,
// but WITHOUT ANY WARRANTY; without even the implied warranty of
// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
// GNU General Public License for more details.

// You should have received a copy of the GNU General Public License
// along with this program.  If not, see <http://www.gnu.org/licenses/>.

pragma solidity ^0.7.0;

import "./BalancerErrors.sol";
import "./IAuthentication.sol";

/**
 * @dev Building block for performing access control on external functions.
 *
 * This contract is used via the `authenticate` modifier (or the `_authenticateCaller` function), which can be applied
 * to external functions to only make them callable by authorized accounts.
 *
 * Derived contracts must implement the `_canPerform` function, which holds the actual access control logic.
 */
abstract contract Authentication is IAuthentication {
    bytes32 private immutable _actionIdDisambiguator;

    /**
     * @dev The main purpose of the `actionIdDisambiguator` is to prevent accidental function selector collisions in
     * multi contract systems.
     *
     * There are two main uses for it:
     *  - if the contract is a singleton, any unique identifier can be used to make the associated action identifiers
     *    unique. The contract's own address is a good option.
     *  - if the contract belongs to a family that shares action identifiers for the same functions, an identifier
     *    shared by the entire family (and no other contract) should be used instead.
     */
    constructor(bytes32 actionIdDisambiguator) {
        _actionIdDisambiguator = actionIdDisambiguator;
    }

    /**
     * @dev Reverts unless the caller is allowed to call this function. Should only be applied to external functions.
     */
    modifier authenticate() {
        _authenticateCaller();
        _;
    }

    /**
     * @dev Reverts unless the caller is allowed to call the entry point function.
     */
    function _authenticateCaller() internal view {
        bytes32 actionId = getActionId(msg.sig);
        _require(_canPerform(actionId, msg.sender), Errors.SENDER_NOT_ALLOWED);
    }

    function getActionId(bytes4 selector) public view override returns (bytes32) {
        // Each external function is dynamically assigned an action identifier as the hash of the disambiguator and the
        // function selector. Disambiguation is necessary to avoid potential collisions in the function selectors of
        // multiple contracts.
        return keccak256(abi.encodePacked(_actionIdDisambiguator, selector));
    }

    function _canPerform(bytes32 actionId, address user) internal view virtual returns (bool);
}

// File: contracts/balancer-core-v2/lib/openzeppelin/ReentrancyGuard.sol



// SPDX-License-Identifier: MIT

// Based on the ReentrancyGuard library from OpenZeppelin Contracts, altered to reduce bytecode size.
// Modifier code is inlined by the compiler, which causes its code to appear multiple times in the codebase. By using
// private functions, we achieve the same end result with slightly higher runtime gas costs, but reduced bytecode size.

pragma solidity ^0.7.0;

import "../helpers/BalancerErrors.sol";

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

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

    uint256 private _status;

    constructor() {
        _status = _NOT_ENTERED;
    }

    /**
     * @dev Prevents a contract from calling itself, directly or indirectly.
     * Calling a `nonReentrant` function from another `nonReentrant`
     * function is not supported. It is possible to prevent this from happening
     * by making the `nonReentrant` function external, and make it call a
     * `private` function that does the actual work.
     */
    modifier nonReentrant() {
        _enterNonReentrant();
        _;
        _exitNonReentrant();
    }

    function _enterNonReentrant() private {
        // On the first call to nonReentrant, _status will be _NOT_ENTERED
        _require(_status != _ENTERED, Errors.REENTRANCY);

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

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

// File: contracts/balancer-core-v2/lib/openzeppelin/SafeERC20.sol



// SPDX-License-Identifier: MIT

// Based on the ReentrancyGuard library from OpenZeppelin Contracts, altered to reduce gas costs.
// The `safeTransfer` and `safeTransferFrom` functions assume that `token` is a contract (an account with code), and
// work differently from the OpenZeppelin version if it is not.

pragma solidity ^0.7.0;

import "../helpers/BalancerErrors.sol";

import "./IERC20.sol";

/**
 * @title SafeERC20
 * @dev Wrappers around ERC20 operations that throw on failure (when the token
 * contract returns false). Tokens that return no value (and instead revert or
 * throw on failure) are also supported, non-reverting calls are assumed to be
 * successful.
 * To use this library you can add a `using SafeERC20 for IERC20;` statement to your contract,
 * which allows you to call the safe operations as `token.safeTransfer(...)`, etc.
 */
library SafeERC20 {
    function safeTransfer(
        IERC20 token,
        address to,
        uint256 value
    ) internal {
        _callOptionalReturn(address(token), abi.encodeWithSelector(token.transfer.selector, to, value));
    }

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

    /**
     * @dev Imitates a Solidity high-level call (i.e. a regular function call to a contract), relaxing the requirement
     * on the return value: the return value is optional (but if data is returned, it must not be false).
     *
     * WARNING: `token` is assumed to be a contract: calls to EOAs will *not* revert.
     */
    function _callOptionalReturn(address token, bytes memory data) private {
        // We need to perform a low level call here, to bypass Solidity's return data size checking mechanism, since
        // we're implementing it ourselves.
        (bool success, bytes memory returndata) = token.call(data);

        // If the low-level call didn't succeed we return whatever was returned from it.
        assembly {
            if eq(success, 0) {
                returndatacopy(0, 0, returndatasize())
                revert(0, returndatasize())
            }
        }

        // Finally we check the returndata size is either zero or true - note that this check will always pass for EOAs
        _require(returndata.length == 0 || abi.decode(returndata, (bool)), Errors.SAFE_ERC20_CALL_FAILED);
    }
}

// File: contracts/balancer-core-v2/lib/helpers/IAuthentication.sol



// SPDX-License-Identifier: GPL-3.0-or-later
// This program is free software: you can redistribute it and/or modify
// it under the terms of the GNU General Public License as published by
// the Free Software Foundation, either version 3 of the License, or
// (at your option) any later version.

// This program is distributed in the hope that it will be useful,
// but WITHOUT ANY WARRANTY; without even the implied warranty of
// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
// GNU General Public License for more details.

// You should have received a copy of the GNU General Public License
// along with this program.  If not, see <http://www.gnu.org/licenses/>.

pragma solidity ^0.7.0;

interface IAuthentication {
    /**
     * @dev Returns the action identifier associated with the external function described by `selector`.
     */
    function getActionId(bytes4 selector) external view returns (bytes32);
}

// File: contracts/balancer-core-v2/lib/math/Math.sol



// SPDX-License-Identifier: MIT

pragma solidity ^0.7.0;

import "../helpers/BalancerErrors.sol";

/**
 * @dev Wrappers over Solidity's arithmetic operations with added overflow checks.
 * Adapted from OpenZeppelin's SafeMath library
 */
library Math {
    /**
     * @dev Returns the addition of two unsigned integers of 256 bits, reverting on overflow.
     */
    function add(uint256 a, uint256 b) internal pure returns (uint256) {
        uint256 c = a + b;
        _require(c >= a, Errors.ADD_OVERFLOW);
        return c;
    }

    /**
     * @dev Returns the addition of two signed integers, reverting on overflow.
     */
    function add(int256 a, int256 b) internal pure returns (int256) {
        int256 c = a + b;
        _require((b >= 0 && c >= a) || (b < 0 && c < a), Errors.ADD_OVERFLOW);
        return c;
    }

    /**
     * @dev Returns the subtraction of two unsigned integers of 256 bits, reverting on overflow.
     */
    function sub(uint256 a, uint256 b) internal pure returns (uint256) {
        _require(b <= a, Errors.SUB_OVERFLOW);
        uint256 c = a - b;
        return c;
    }

    /**
     * @dev Returns the subtraction of two signed integers, reverting on overflow.
     */
    function sub(int256 a, int256 b) internal pure returns (int256) {
        int256 c = a - b;
        _require((b >= 0 && c <= a) || (b < 0 && c > a), Errors.SUB_OVERFLOW);
        return c;
    }

    /**
     * @dev Returns the largest of two numbers of 256 bits.
     */
    function max(uint256 a, uint256 b) internal pure returns (uint256) {
        return a >= b ? a : b;
    }

    /**
     * @dev Returns the smallest of two numbers of 256 bits.
     */
    function min(uint256 a, uint256 b) internal pure returns (uint256) {
        return a < b ? a : b;
    }

    function mul(uint256 a, uint256 b) internal pure returns (uint256) {
        uint256 c = a * b;
        _require(a == 0 || c / a == b, Errors.MUL_OVERFLOW);
        return c;
    }

    function divDown(uint256 a, uint256 b) internal pure returns (uint256) {
        _require(b != 0, Errors.ZERO_DIVISION);
        return a / b;
    }

    function divUp(uint256 a, uint256 b) internal pure returns (uint256) {
        _require(b != 0, Errors.ZERO_DIVISION);

        if (a == 0) {
            return 0;
        } else {
            return 1 + (a - 1) / b;
        }
    }
}

// File: contracts/balancer-core-v2/lib/openzeppelin/IERC20Permit.sol



// SPDX-License-Identifier: MIT

pragma solidity ^0.7.0;

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

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

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

// File: contracts/balancer-core-v2/lib/openzeppelin/EIP712.sol



// SPDX-License-Identifier: MIT

pragma solidity ^0.7.0;

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

    /* solhint-enable var-name-mixedcase */

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

    /**
     * @dev Returns the domain separator for the current chain.
     */
    function _domainSeparatorV4() internal view virtual returns (bytes32) {
        return keccak256(abi.encode(_TYPE_HASH, _HASHED_NAME, _HASHED_VERSION, _getChainId(), address(this)));
    }

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

    function _getChainId() private view returns (uint256 chainId) {
        // Silence state mutability warning without generating bytecode.
        // See https://github.com/ethereum/solidity/issues/10090#issuecomment-741789128 and
        // https://github.com/ethereum/solidity/issues/2691
        this;

        // solhint-disable-next-line no-inline-assembly
        assembly {
            chainId := chainid()
        }
    }
}