// File: @balancer-labs/v2-interfaces/contracts/pool-utils/IVersion.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 <0.9.0;

/**
 * @notice Simple interface to retrieve the version of a deployed contract.
 */
interface IVersion {
    /**
     * @dev Returns a JSON representation of the contract version containing name, version number and task ID.
     */
    function version() external view returns (string memory);
}

// File: @balancer-labs/v2-interfaces/contracts/vault/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 "../solidity-utils/openzeppelin/IERC20.sol";
import "../solidity-utils/helpers/IAuthentication.sol";
import "../solidity-utils/helpers/ISignaturesValidator.sol";
import "../solidity-utils/helpers/ITemporarilyPausable.sol";
import "../solidity-utils/misc/IWETH.sol";

import "./IAsset.sol";
import "./IAuthorizer.sol";
import "./IFlashLoanRecipient.sol";
import "./IProtocolFeesCollector.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, IAuthentication {
    // 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 (IProtocolFeesCollector);

    /**
     * @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/ComposableStablePool.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 "@balancer-labs/v2-interfaces/contracts/pool-stable/StablePoolUserData.sol";
import "@balancer-labs/v2-interfaces/contracts/solidity-utils/helpers/BalancerErrors.sol";
import "@balancer-labs/v2-interfaces/contracts/standalone-utils/IProtocolFeePercentagesProvider.sol";
import "@balancer-labs/v2-interfaces/contracts/pool-utils/IRateProvider.sol";
import "@balancer-labs/v2-interfaces/contracts/pool-utils/IVersion.sol";

import "@balancer-labs/v2-solidity-utils/contracts/math/FixedPoint.sol";
import "@balancer-labs/v2-solidity-utils/contracts/math/Math.sol";
import "@balancer-labs/v2-solidity-utils/contracts/helpers/ERC20Helpers.sol";
import "@balancer-labs/v2-solidity-utils/contracts/helpers/InputHelpers.sol";

import "@balancer-labs/v2-pool-utils/contracts/BaseGeneralPool.sol";
import "@balancer-labs/v2-pool-utils/contracts/rates/PriceRateCache.sol";

import "./ComposableStablePoolStorage.sol";
import "./ComposableStablePoolRates.sol";
import "./ComposableStablePoolStorage.sol";
import "./ComposableStablePoolRates.sol";
import "./ComposableStablePoolProtocolFees.sol";
import "./StablePoolAmplification.sol";
import "./StableMath.sol";

/**
 * @dev StablePool with preminted BPT and rate providers for each token, allowing for e.g. wrapped tokens with a known
 * price ratio, such as Compound's cTokens.
 *
 * BPT is preminted on Pool initialization and registered as one of the Pool's tokens, allowing for swaps to behave as
 * single-token joins or exits (by swapping a token for BPT). We also support regular joins and exits, which can mint
 * and burn BPT.
 *
 * Preminted BPT is deposited in the Vault as the initial balance of the Pool, and doesn't belong to any entity until
 * transferred out of the Pool. The Pool's arithmetic behaves as if it didn't exist, and the BPT total supply is not
 * a useful value: we rely on the 'virtual supply' (how much BPT is actually owned outside the Vault) instead.
 */
contract ComposableStablePool is
    IRateProvider,
    IVersion,
    BaseGeneralPool,
    StablePoolAmplification,
    ComposableStablePoolRates,
    ComposableStablePoolProtocolFees
{
    using FixedPoint for uint256;
    using PriceRateCache for bytes32;
    using StablePoolUserData for bytes;
    using BasePoolUserData for bytes;

    // The maximum imposed by the Vault, which stores balances in a packed format, is 2**(112) - 1.
    // We are preminting half of that value (rounded up).
    uint256 private constant _PREMINTED_TOKEN_BALANCE = 2**(111);

    string private _version;

    // The constructor arguments are received in a struct to work around stack-too-deep issues
    struct NewPoolParams {
        IVault vault;
        IProtocolFeePercentagesProvider protocolFeeProvider;
        string name;
        string symbol;
        IERC20[] tokens;
        IRateProvider[] rateProviders;
        uint256[] tokenRateCacheDurations;
        bool exemptFromYieldProtocolFeeFlag;
        uint256 amplificationParameter;
        uint256 swapFeePercentage;
        uint256 pauseWindowDuration;
        uint256 bufferPeriodDuration;
        address owner;
        string version;
    }

    constructor(NewPoolParams memory params)
        BasePool(
            params.vault,
            IVault.PoolSpecialization.GENERAL,
            params.name,
            params.symbol,
            _insertSorted(params.tokens, IERC20(this)),
            new address[](params.tokens.length + 1),
            params.swapFeePercentage,
            params.pauseWindowDuration,
            params.bufferPeriodDuration,
            params.owner
        )
        StablePoolAmplification(params.amplificationParameter)
        ComposableStablePoolStorage(_extractStorageParams(params))
        ComposableStablePoolRates(_extractRatesParams(params))
        ProtocolFeeCache(params.protocolFeeProvider, ProtocolFeeCache.DELEGATE_PROTOCOL_SWAP_FEES_SENTINEL)
    {
        _version = params.version;
    }

    // Translate parameters to avoid stack-too-deep issues in the constructor
    function _extractRatesParams(NewPoolParams memory params)
        private
        pure
        returns (ComposableStablePoolRates.RatesParams memory)
    {
        return
            ComposableStablePoolRates.RatesParams({
                tokens: params.tokens,
                rateProviders: params.rateProviders,
                tokenRateCacheDurations: params.tokenRateCacheDurations
            });
    }

    // Translate parameters to avoid stack-too-deep issues in the constructor
    function _extractStorageParams(NewPoolParams memory params)
        private
        view
        returns (ComposableStablePoolStorage.StorageParams memory)
    {
        return
            ComposableStablePoolStorage.StorageParams({
                registeredTokens: _insertSorted(params.tokens, IERC20(this)),
                tokenRateProviders: params.rateProviders,
                exemptFromYieldProtocolFeeFlag: params.exemptFromYieldProtocolFeeFlag
            });
    }

    function version() external view override returns (string memory) {
        return _version;
    }

    /**
     * @notice Return the minimum BPT balance, required to avoid minimum token balances.
     * @dev This amount is minted and immediately burned on pool initialization, so that the total supply
     * (and therefore post-exit token balances), can never be zero. This keeps the math well-behaved when
     * liquidity is low. (It also provides an easy way to check whether a pool has been initialized, to
     * ensure this is only done once.)
     */
    function getMinimumBpt() external pure returns (uint256) {
        return _getMinimumBpt();
    }

    // BasePool hook

    /**
     * @dev Override base pool hook invoked before any swap, join, or exit to ensure rates are updated before
     * the operation.
     */
    function _beforeSwapJoinExit() internal override {
        super._beforeSwapJoinExit();

        // Before the scaling factors are read, we must update the cached rates, as those will be used to compute the
        // scaling factors.
        // Note that this is not done in a recovery mode exit (since _beforeSwapjoinExit() is not called under those
        // conditions), but this is fine as recovery mode exits are unaffected by scaling factors anyway.
        _cacheTokenRatesIfNecessary();
    }

    // Swap Hooks

    /**
     * @dev Override this hook called by the base class `onSwap`, to check whether we are doing a regular swap,
     * or a swap involving BPT, which is equivalent to a single token join or exit. Since one of the Pool's
     * tokens is the preminted BPT, we need to handle swaps where BPT is involved separately.
     *
     * At this point, the balances are unscaled. The indices are coming from the Vault, so they are indices into
     * the array of registered tokens (including BPT).
     *
     * If this is a swap involving BPT, call `_swapWithBpt`, which computes the amountOut using the swapFeePercentage
     * and charges protocol fees, in the same manner as single token join/exits. Otherwise, perform the default
     * processing for a regular swap.
     */
    function _swapGivenIn(
        SwapRequest memory swapRequest,
        uint256[] memory registeredBalances,
        uint256 registeredIndexIn,
        uint256 registeredIndexOut,
        uint256[] memory scalingFactors
    ) internal virtual override returns (uint256) {
        return
            (swapRequest.tokenIn == IERC20(this) || swapRequest.tokenOut == IERC20(this))
                ? _swapWithBpt(swapRequest, registeredBalances, registeredIndexIn, registeredIndexOut, scalingFactors)
                : super._swapGivenIn(
                    swapRequest,
                    registeredBalances,
                    registeredIndexIn,
                    registeredIndexOut,
                    scalingFactors
                );
    }

    /**
     * @dev Override this hook called by the base class `onSwap`, to check whether we are doing a regular swap,
     * or a swap involving BPT, which is equivalent to a single token join or exit. Since one of the Pool's
     * tokens is the preminted BPT, we need to handle swaps where BPT is involved separately.
     *
     * At this point, the balances are unscaled. The indices and balances are coming from the Vault, so they
     * refer to the full set of registered tokens (including BPT).
     *
     * If this is a swap involving BPT, call `_swapWithBpt`, which computes the amountOut using the swapFeePercentage
     * and charges protocol fees, in the same manner as single token join/exits. Otherwise, perform the default
     * processing for a regular swap.
     */
    function _swapGivenOut(
        SwapRequest memory swapRequest,
        uint256[] memory registeredBalances,
        uint256 registeredIndexIn,
        uint256 registeredIndexOut,
        uint256[] memory scalingFactors
    ) internal virtual override returns (uint256) {
        return
            (swapRequest.tokenIn == IERC20(this) || swapRequest.tokenOut == IERC20(this))
                ? _swapWithBpt(swapRequest, registeredBalances, registeredIndexIn, registeredIndexOut, scalingFactors)
                : super._swapGivenOut(
                    swapRequest,
                    registeredBalances,
                    registeredIndexIn,
                    registeredIndexOut,
                    scalingFactors
                );
    }

    /**
     * @dev This is called from the base class `_swapGivenIn`, so at this point the amount has been adjusted
     * for swap fees, and balances have had scaling applied. This will only be called for regular (non-BPT) swaps,
     * so forward to `onRegularSwap`.
     */
    function _onSwapGivenIn(
        SwapRequest memory request,
        uint256[] memory registeredBalances,
        uint256 registeredIndexIn,
        uint256 registeredIndexOut
    ) internal virtual override returns (uint256) {
        return
            _onRegularSwap(
                true, // given in
                request.amount,
                registeredBalances,
                registeredIndexIn,
                registeredIndexOut
            );
    }

    /**
     * @dev This is called from the base class `_swapGivenOut`, so at this point the amount has been adjusted
     * for swap fees, and balances have had scaling applied. This will only be called for regular (non-BPT) swaps,
     * so forward to `onRegularSwap`.
     */
    function _onSwapGivenOut(
        SwapRequest memory request,
        uint256[] memory registeredBalances,
        uint256 registeredIndexIn,
        uint256 registeredIndexOut
    ) internal virtual override returns (uint256) {
        return
            _onRegularSwap(
                false, // given out
                request.amount,
                registeredBalances,
                registeredIndexIn,
                registeredIndexOut
            );
    }

    /**
     * @dev Perform a swap between non-BPT tokens. Scaling and fee adjustments have been performed upstream, so
     * all we need to do here is calculate the price quote, depending on the direction of the swap.
     */
    function _onRegularSwap(
        bool isGivenIn,
        uint256 amountGiven,
        uint256[] memory registeredBalances,
        uint256 registeredIndexIn,
        uint256 registeredIndexOut
    ) private view returns (uint256) {
        // Adjust indices and balances for BPT token
        uint256[] memory balances = _dropBptItem(registeredBalances);
        uint256 indexIn = _skipBptIndex(registeredIndexIn);
        uint256 indexOut = _skipBptIndex(registeredIndexOut);

        (uint256 currentAmp, ) = _getAmplificationParameter();
        uint256 invariant = StableMath._calculateInvariant(currentAmp, balances);

        if (isGivenIn) {
            return StableMath._calcOutGivenIn(currentAmp, balances, indexIn, indexOut, amountGiven, invariant);
        } else {
            return StableMath._calcInGivenOut(currentAmp, balances, indexIn, indexOut, amountGiven, invariant);
        }
    }

    /**
     * @dev Perform a swap involving the BPT token, equivalent to a single-token join or exit. As with the standard
     * joins and swaps, we first pay any protocol fees pending from swaps that occurred since the previous join or
     * exit, then perform the operation (joinSwap or exitSwap), and finally store the "post operation" invariant and
     * amp, which establishes the new basis for protocol fees.
     *
     * At this point, the scaling factors (including rates) have been computed by the base class, but not yet applied
     * to the balances.
     */
    function _swapWithBpt(
        SwapRequest memory swapRequest,
        uint256[] memory registeredBalances,
        uint256 registeredIndexIn,
        uint256 registeredIndexOut,
        uint256[] memory scalingFactors
    ) private returns (uint256) {
        bool isGivenIn = swapRequest.kind == IVault.SwapKind.GIVEN_IN;

        _upscaleArray(registeredBalances, scalingFactors);
        swapRequest.amount = _upscale(
            swapRequest.amount,
            scalingFactors[isGivenIn ? registeredIndexIn : registeredIndexOut]
        );

        (
            uint256 preJoinExitSupply,
            uint256[] memory balances,
            uint256 currentAmp,
            uint256 preJoinExitInvariant
        ) = _beforeJoinExit(registeredBalances);

        // These calls mutate `balances` so that it holds the post join-exit balances.
        (uint256 amountCalculated, uint256 postJoinExitSupply) = registeredIndexOut == getBptIndex()
            ? _doJoinSwap(
                isGivenIn,
                swapRequest.amount,
                balances,
                _skipBptIndex(registeredIndexIn),
                currentAmp,
                preJoinExitSupply,
                preJoinExitInvariant
            )
            : _doExitSwap(
                isGivenIn,
                swapRequest.amount,
                balances,
                _skipBptIndex(registeredIndexOut),
                currentAmp,
                preJoinExitSupply,
                preJoinExitInvariant
            );

        _updateInvariantAfterJoinExit(
            currentAmp,
            balances,
            preJoinExitInvariant,
            preJoinExitSupply,
            postJoinExitSupply
        );

        return
            isGivenIn
                ? _downscaleDown(amountCalculated, scalingFactors[registeredIndexOut]) // Amount out, round down
                : _downscaleUp(amountCalculated, scalingFactors[registeredIndexIn]); // Amount in, round up
    }

    /**
     * @dev This mutates `balances` so that they become the post-joinswap balances. The StableMath interfaces
     * are different depending on the swap direction, so we forward to the appropriate low-level join function.
     */
    function _doJoinSwap(
        bool isGivenIn,
        uint256 amount,
        uint256[] memory balances,
        uint256 indexIn,
        uint256 currentAmp,
        uint256 actualSupply,
        uint256 preJoinExitInvariant
    ) internal view returns (uint256, uint256) {
        return
            isGivenIn
                ? _joinSwapExactTokenInForBptOut(
                    amount,
                    balances,
                    indexIn,
                    currentAmp,
                    actualSupply,
                    preJoinExitInvariant
                )
                : _joinSwapExactBptOutForTokenIn(
                    amount,
                    balances,
                    indexIn,
                    currentAmp,
                    actualSupply,
                    preJoinExitInvariant
                );
    }

    /**
     * @dev Since this is a join, we know the tokenOut is BPT. Since it is GivenIn, we know the tokenIn amount,
     * and must calculate the BPT amount out.
     * We are moving preminted BPT out of the Vault, which increases the virtual supply.
     */
    function _joinSwapExactTokenInForBptOut(
        uint256 amountIn,
        uint256[] memory balances,
        uint256 indexIn,
        uint256 currentAmp,
        uint256 actualSupply,
        uint256 preJoinExitInvariant
    ) internal view returns (uint256, uint256) {
        // The StableMath function was created with joins in mind, so it expects a full amounts array. We create an
        // empty one and only set the amount for the token involved.
        uint256[] memory amountsIn = new uint256[](balances.length);
        amountsIn[indexIn] = amountIn;

        uint256 bptOut = StableMath._calcBptOutGivenExactTokensIn(
            currentAmp,
            balances,
            amountsIn,
            actualSupply,
            preJoinExitInvariant,
            getSwapFeePercentage()
        );

        balances[indexIn] = balances[indexIn].add(amountIn);
        uint256 postJoinExitSupply = actualSupply.add(bptOut);

        return (bptOut, postJoinExitSupply);
    }

    /**
     * @dev Since this is a join, we know the tokenOut is BPT. Since it is GivenOut, we know the BPT amount,
     * and must calculate the token amount in.
     * We are moving preminted BPT out of the Vault, which increases the virtual supply.
     */
    function _joinSwapExactBptOutForTokenIn(
        uint256 bptOut,
        uint256[] memory balances,
        uint256 indexIn,
        uint256 currentAmp,
        uint256 actualSupply,
        uint256 preJoinExitInvariant
    ) internal view returns (uint256, uint256) {
        uint256 amountIn = StableMath._calcTokenInGivenExactBptOut(
            currentAmp,
            balances,
            indexIn,
            bptOut,
            actualSupply,
            preJoinExitInvariant,
            getSwapFeePercentage()
        );

        balances[indexIn] = balances[indexIn].add(amountIn);
        uint256 postJoinExitSupply = actualSupply.add(bptOut);

        return (amountIn, postJoinExitSupply);
    }

    /**
     * @dev This mutates balances so that they become the post-exitswap balances. The StableMath interfaces are
     * different depending on the swap direction, so we forward to the appropriate low-level exit function.
     */
    function _doExitSwap(
        bool isGivenIn,
        uint256 amount,
        uint256[] memory balances,
        uint256 indexOut,
        uint256 currentAmp,
        uint256 actualSupply,
        uint256 preJoinExitInvariant
    ) internal view returns (uint256, uint256) {
        return
            isGivenIn
                ? _exitSwapExactBptInForTokenOut(
                    amount,
                    balances,
                    indexOut,
                    currentAmp,
                    actualSupply,
                    preJoinExitInvariant
                )
                : _exitSwapExactTokenOutForBptIn(
                    amount,
                    balances,
                    indexOut,
                    currentAmp,
                    actualSupply,
                    preJoinExitInvariant
                );
    }

    /**
     * @dev Since this is an exit, we know the tokenIn is BPT. Since it is GivenIn, we know the BPT amount,
     * and must calculate the token amount out.
     * We are moving BPT out of circulation and into the Vault, which decreases the virtual supply.
     */
    function _exitSwapExactBptInForTokenOut(
        uint256 bptAmount,
        uint256[] memory balances,
        uint256 indexOut,
        uint256 currentAmp,
        uint256 actualSupply,
        uint256 preJoinExitInvariant
    ) internal view returns (uint256, uint256) {
        uint256 amountOut = StableMath._calcTokenOutGivenExactBptIn(
            currentAmp,
            balances,
            indexOut,
            bptAmount,
            actualSupply,
            preJoinExitInvariant,
            getSwapFeePercentage()
        );

        balances[indexOut] = balances[indexOut].sub(amountOut);
        uint256 postJoinExitSupply = actualSupply.sub(bptAmount);

        return (amountOut, postJoinExitSupply);
    }

    /**
     * @dev Since this is an exit, we know the tokenIn is BPT. Since it is GivenOut, we know the token amount out,
     * and must calculate the BPT amount in.
     * We are moving BPT out of circulation and into the Vault, which decreases the virtual supply.
     */
    function _exitSwapExactTokenOutForBptIn(
        uint256 amountOut,
        uint256[] memory balances,
        uint256 indexOut,
        uint256 currentAmp,
        uint256 actualSupply,
        uint256 preJoinExitInvariant
    ) internal view returns (uint256, uint256) {
        // The StableMath function was created with exits in mind, so it expects a full amounts array. We create an
        // empty one and only set the amount for the token involved.
        uint256[] memory amountsOut = new uint256[](balances.length);
        amountsOut[indexOut] = amountOut;

        uint256 bptAmount = StableMath._calcBptInGivenExactTokensOut(
            currentAmp,
            balances,
            amountsOut,
            actualSupply,
            preJoinExitInvariant,
            getSwapFeePercentage()
        );

        balances[indexOut] = balances[indexOut].sub(amountOut);
        uint256 postJoinExitSupply = actualSupply.sub(bptAmount);

        return (bptAmount, postJoinExitSupply);
    }

    // Join Hooks

    /**
     * Since this Pool has preminted BPT which is stored in the Vault, it cannot simply be minted at construction.
     *
     * We take advantage of the fact that StablePools have an initialization step where BPT is minted to the first
     * account joining them, and perform both actions at once. By minting the entire BPT supply for the initial joiner
     * and then pulling all tokens except those due the joiner, we arrive at the desired state of the Pool holding all
     * BPT except the joiner's.
     */
    function _onInitializePool(
        bytes32,
        address sender,
        address,
        uint256[] memory scalingFactors,
        bytes memory userData
    ) internal override returns (uint256, uint256[] memory) {
        StablePoolUserData.JoinKind kind = userData.joinKind();
        _require(kind == StablePoolUserData.JoinKind.INIT, Errors.UNINITIALIZED);

        // AmountsIn usually does not include the BPT token; initialization is the one time it has to.
        uint256[] memory amountsInIncludingBpt = userData.initialAmountsIn();
        InputHelpers.ensureInputLengthMatch(amountsInIncludingBpt.length, scalingFactors.length);
        _upscaleArray(amountsInIncludingBpt, scalingFactors);

        (uint256 amp, ) = _getAmplificationParameter();
        uint256[] memory amountsIn = _dropBptItem(amountsInIncludingBpt);
        uint256 invariantAfterJoin = StableMath._calculateInvariant(amp, amountsIn);

        // Set the initial BPT to the value of the invariant
        uint256 bptAmountOut = invariantAfterJoin;

        // BasePool will mint bptAmountOut for the sender: we then also mint the remaining BPT to make up the total
        // supply, and have the Vault pull those tokens from the sender as part of the join.
        // We are only minting half of the maximum value - already an amount many orders of magnitude greater than any
        // conceivable real liquidity - to allow for minting new BPT as a result of regular joins.
        //
        // Note that the sender need not approve BPT for the Vault as the Vault already has infinite BPT allowance for
        // all accounts.
        uint256 initialBpt = _PREMINTED_TOKEN_BALANCE.sub(bptAmountOut);

        _mintPoolTokens(sender, initialBpt);
        amountsInIncludingBpt[getBptIndex()] = initialBpt;

        // Initialization is still a join, so we need to do post-join work.
        _updatePostJoinExit(amp, invariantAfterJoin);

        return (bptAmountOut, amountsInIncludingBpt);
    }

    /**
     * @dev Base pool hook called from `onJoinPool`. Forward to `onJoinExitPool` with `isJoin` set to true.
     */
    function _onJoinPool(
        bytes32,
        address,
        address,
        uint256[] memory registeredBalances,
        uint256,
        uint256,
        uint256[] memory scalingFactors,
        bytes memory userData
    ) internal override returns (uint256, uint256[] memory) {
        return _onJoinExitPool(true, registeredBalances, scalingFactors, userData);
    }

    /**
     * @dev Base pool hook called from `onExitPool`. Forward to `onJoinExitPool` with `isJoin` set to false.
     * Note that recovery mode exits do not call `_onExitPool`.
     */
    function _onExitPool(
        bytes32,
        address,
        address,
        uint256[] memory registeredBalances,
        uint256,
        uint256,
        uint256[] memory scalingFactors,
        bytes memory userData
    ) internal override returns (uint256, uint256[] memory) {
        return _onJoinExitPool(false, registeredBalances, scalingFactors, userData);
    }

    /**
     * @dev Pay protocol fees before the operation, and call `_updateInvariantAfterJoinExit` afterward, to establish
     * the new basis for protocol fees.
     */
    function _onJoinExitPool(
        bool isJoin,
        uint256[] memory registeredBalances,
        uint256[] memory scalingFactors,
        bytes memory userData
    ) internal returns (uint256, uint256[] memory) {
        (
            uint256 preJoinExitSupply,
            uint256[] memory balances,
            uint256 currentAmp,
            uint256 preJoinExitInvariant
        ) = _beforeJoinExit(registeredBalances);


            function(uint256[] memory, uint256, uint256, uint256, uint256[] memory, bytes memory)
                internal
                view
                returns (uint256, uint256[] memory) _doJoinOrExit
         = (isJoin ? _doJoin : _doExit);

        (uint256 bptAmount, uint256[] memory amountsDelta) = _doJoinOrExit(
            balances,
            currentAmp,
            preJoinExitSupply,
            preJoinExitInvariant,
            scalingFactors,
            userData
        );

        // Unlike joinswaps, explicit joins do not mutate balances into the post join-exit balances so we must perform
        // this mutation here.
        function(uint256, uint256) internal pure returns (uint256) _addOrSub = isJoin ? FixedPoint.add : FixedPoint.sub;
        _mutateAmounts(balances, amountsDelta, _addOrSub);
        uint256 postJoinExitSupply = _addOrSub(preJoinExitSupply, bptAmount);

        // Pass in the post-join balances to reset the protocol fee basis.
        // We are minting bptAmount, increasing the total (and virtual) supply post-join
        _updateInvariantAfterJoinExit(
            currentAmp,
            balances,
            preJoinExitInvariant,
            preJoinExitSupply,
            postJoinExitSupply
        );

        // For clarity and simplicity, arrays used and computed in lower level functions do not include BPT.
        // But the amountsIn array passed back to the Vault must include BPT, so we add it back in here.
        return (bptAmount, _addBptItem(amountsDelta, 0));
    }

    /**
     * @dev Pay any due protocol fees and calculate values necessary for performing the join/exit.
     */
    function _beforeJoinExit(uint256[] memory registeredBalances)
        internal
        returns (
            uint256,
            uint256[] memory,
            uint256,
            uint256
        )
    {
        (uint256 lastJoinExitAmp, uint256 lastPostJoinExitInvariant) = getLastJoinExitData();
        (
            uint256 preJoinExitSupply,
            uint256[] memory balances,
            uint256 oldAmpPreJoinExitInvariant
        ) = _payProtocolFeesBeforeJoinExit(registeredBalances, lastJoinExitAmp, lastPostJoinExitInvariant);

        // If the amplification factor is the same as it was during the last join/exit then we can reuse the
        // value calculated using the "old" amplification factor. If not, then we have to calculate this now.
        (uint256 currentAmp, ) = _getAmplificationParameter();
        uint256 preJoinExitInvariant = currentAmp == lastJoinExitAmp
            ? oldAmpPreJoinExitInvariant
            : StableMath._calculateInvariant(currentAmp, balances);

        return (preJoinExitSupply, balances, currentAmp, preJoinExitInvariant);
    }

    /**
     * @dev Support single- and multi-token joins, plus explicit proportional joins.
     */
    function _doJoin(
        uint256[] memory balances,
        uint256 currentAmp,
        uint256 preJoinExitSupply,
        uint256 preJoinExitInvariant,
        uint256[] memory scalingFactors,
        bytes memory userData
    ) internal view returns (uint256, uint256[] memory) {
        StablePoolUserData.JoinKind kind = userData.joinKind();
        if (kind == StablePoolUserData.JoinKind.EXACT_TOKENS_IN_FOR_BPT_OUT) {
            return
                _joinExactTokensInForBPTOut(
                    preJoinExitSupply,
                    preJoinExitInvariant,
                    currentAmp,
                    balances,
                    scalingFactors,
                    userData
                );
        } else if (kind == StablePoolUserData.JoinKind.ALL_TOKENS_IN_FOR_EXACT_BPT_OUT) {
            return _joinAllTokensInForExactBptOut(preJoinExitSupply, balances, userData);
        } else if (kind == StablePoolUserData.JoinKind.TOKEN_IN_FOR_EXACT_BPT_OUT) {
            return _joinTokenInForExactBPTOut(preJoinExitSupply, preJoinExitInvariant, currentAmp, balances, userData);
        } else {
            _revert(Errors.UNHANDLED_JOIN_KIND);
        }
    }

    /**
     * @dev Proportional join. Pays no swap fees.
     */
    function _joinAllTokensInForExactBptOut(
        uint256 actualSupply,
        uint256[] memory balances,
        bytes memory userData
    ) private pure returns (uint256, uint256[] memory) {
        uint256 bptAmountOut = userData.allTokensInForExactBptOut();
        uint256[] memory amountsIn = StableMath._computeProportionalAmountsIn(balances, bptAmountOut, actualSupply);

        return (bptAmountOut, amountsIn);
    }

    /**
     * @dev Multi-token join. Joins with proportional amounts will pay no protocol fees.
     */
    function _joinExactTokensInForBPTOut(
        uint256 actualSupply,
        uint256 preJoinExitInvariant,
        uint256 currentAmp,
        uint256[] memory balances,
        uint256[] memory scalingFactors,
        bytes memory userData
    ) private view returns (uint256, uint256[] memory) {
        (uint256[] memory amountsIn, uint256 minBPTAmountOut) = userData.exactTokensInForBptOut();
        InputHelpers.ensureInputLengthMatch(balances.length, amountsIn.length);

        // The user-provided amountsIn is unscaled, so we address that.
        _upscaleArray(amountsIn, _dropBptItem(scalingFactors));

        uint256 bptAmountOut = StableMath._calcBptOutGivenExactTokensIn(
            currentAmp,
            balances,
            amountsIn,
            actualSupply,
            preJoinExitInvariant,
            getSwapFeePercentage()
        );

        _require(bptAmountOut >= minBPTAmountOut, Errors.BPT_OUT_MIN_AMOUNT);

        return (bptAmountOut, amountsIn);
    }

    /**
     * @dev Single-token join, equivalent to swapping a pool token for BPT.
     */
    function _joinTokenInForExactBPTOut(
        uint256 actualSupply,
        uint256 preJoinExitInvariant,
        uint256 currentAmp,
        uint256[] memory balances,
        bytes memory userData
    ) private view returns (uint256, uint256[] memory) {
        // Since this index is sent in from the user, we interpret it as NOT including the BPT token.
        (uint256 bptAmountOut, uint256 tokenIndex) = userData.tokenInForExactBptOut();
        // Note that there is no maximum amountIn parameter: this is handled by `IVault.joinPool`.

        // Balances are passed through from the Vault hook, and include BPT
        _require(tokenIndex < balances.length, Errors.OUT_OF_BOUNDS);

        // We join with a single token, so initialize amountsIn with zeros.
        uint256[] memory amountsIn = new uint256[](balances.length);

        // And then assign the result to the selected token.
        amountsIn[tokenIndex] = StableMath._calcTokenInGivenExactBptOut(
            currentAmp,
            balances,
            tokenIndex,
            bptAmountOut,
            actualSupply,
            preJoinExitInvariant,
            getSwapFeePercentage()
        );

        return (bptAmountOut, amountsIn);
    }

    // Exit Hooks

    /**
     * @dev Support single- and multi-token exits, plus explicit proportional exits (in addition to the
     * recovery mode exit).
     */
    function _doExit(
        uint256[] memory balances,
        uint256 currentAmp,
        uint256 preJoinExitSupply,
        uint256 preJoinExitInvariant,
        uint256[] memory scalingFactors,
        bytes memory userData
    ) internal view returns (uint256, uint256[] memory) {
        StablePoolUserData.ExitKind kind = userData.exitKind();
        if (kind == StablePoolUserData.ExitKind.BPT_IN_FOR_EXACT_TOKENS_OUT) {
            return
                _exitBPTInForExactTokensOut(
                    preJoinExitSupply,
                    preJoinExitInvariant,
                    currentAmp,
                    balances,
                    scalingFactors,
                    userData
                );
        } else if (kind == StablePoolUserData.ExitKind.EXACT_BPT_IN_FOR_ALL_TOKENS_OUT) {
            return _exitExactBPTInForTokensOut(preJoinExitSupply, balances, userData);
        } else if (kind == StablePoolUserData.ExitKind.EXACT_BPT_IN_FOR_ONE_TOKEN_OUT) {
            return _exitExactBPTInForTokenOut(preJoinExitSupply, preJoinExitInvariant, currentAmp, balances, userData);
        } else {
            _revert(Errors.UNHANDLED_EXIT_KIND);
        }
    }

    /**
     * @dev Proportional exit. Pays no swap fees. This is functionally equivalent to the recovery mode exit,
     * except this doesn't skip protocol fee collection, calling rate providers, etc., and doesn't require
     * recovery mode to be enabled.
     */
    function _exitExactBPTInForTokensOut(
        uint256 actualSupply,
        uint256[] memory balances,
        bytes memory userData
    ) private pure returns (uint256, uint256[] memory) {
        uint256 bptAmountIn = userData.exactBptInForTokensOut();
        uint256[] memory amountsOut = _computeProportionalAmountsOut(balances, actualSupply, bptAmountIn);

        return (bptAmountIn, amountsOut);
    }

    /**
     * @dev Multi-token exit. Proportional exits will pay no protocol fees.
     */
    function _exitBPTInForExactTokensOut(
        uint256 actualSupply,
        uint256 preJoinExitInvariant,
        uint256 currentAmp,
        uint256[] memory balances,
        uint256[] memory scalingFactors,
        bytes memory userData
    ) private view returns (uint256, uint256[] memory) {
        (uint256[] memory amountsOut, uint256 maxBPTAmountIn) = userData.bptInForExactTokensOut();
        InputHelpers.ensureInputLengthMatch(amountsOut.length, balances.length);

        // The user-provided amountsIn is unscaled, so we address that.
        _upscaleArray(amountsOut, _dropBptItem(scalingFactors));

        uint256 bptAmountIn = StableMath._calcBptInGivenExactTokensOut(
            currentAmp,
            balances,
            amountsOut,
            actualSupply,
            preJoinExitInvariant,
            getSwapFeePercentage()
        );
        _require(bptAmountIn <= maxBPTAmountIn, Errors.BPT_IN_MAX_AMOUNT);

        return (bptAmountIn, amountsOut);
    }

    /**
     * @dev Single-token exit, equivalent to swapping BPT for a pool token.
     */
    function _exitExactBPTInForTokenOut(
        uint256 actualSupply,
        uint256 preJoinExitInvariant,
        uint256 currentAmp,
        uint256[] memory balances,
        bytes memory userData
    ) private view returns (uint256, uint256[] memory) {
        // Since this index is sent in from the user, we interpret it as NOT including the BPT token
        (uint256 bptAmountIn, uint256 tokenIndex) = userData.exactBptInForTokenOut();
        // Note that there is no minimum amountOut parameter: this is handled by `IVault.exitPool`.

        _require(tokenIndex < balances.length, Errors.OUT_OF_BOUNDS);

        // We exit in a single token, so initialize amountsOut with zeros
        uint256[] memory amountsOut = new uint256[](balances.length);

        // And then assign the result to the selected token.
        amountsOut[tokenIndex] = StableMath._calcTokenOutGivenExactBptIn(
            currentAmp,
            balances,
            tokenIndex,
            bptAmountIn,
            actualSupply,
            preJoinExitInvariant,
            getSwapFeePercentage()
        );

        return (bptAmountIn, amountsOut);
    }

    /**
     * @dev We cannot use the default RecoveryMode implementation here, since we need to account for the BPT token.
     */
    function _doRecoveryModeExit(
        uint256[] memory registeredBalances,
        uint256,
        bytes memory userData
    ) internal virtual override returns (uint256, uint256[] memory) {
        // Since this Pool uses preminted BPT, we need to replace the total supply with the virtual total supply, and
        // adjust the balances array by removing BPT from it.
        // Note that we don't compute the actual supply, which would require a lot of complex calculations and
        // interactions with external components. This is fine because virtual and actual supply are the same while
        // recovery mode is enabled (since all protocol fees are forfeit and the fee percentages zeroed out).
        (uint256 virtualSupply, uint256[] memory balances) = _dropBptItemFromBalances(registeredBalances);

        (uint256 bptAmountIn, uint256[] memory amountsOut) = super._doRecoveryModeExit(
            balances,
            virtualSupply,
            userData
        );

        // The vault requires an array including BPT, so add it back in here.
        return (bptAmountIn, _addBptItem(amountsOut, 0));
    }

    // BPT rate

    /**
     * Many functions require accessing multiple internal values that might at first seem unrelated, but are actually
     * quite intertwined, and computed at the same time for optimal performance (since calculating some of them also
     * yields intermediate results useful for other queries). This helper function returns many of these values,
     * greatly reducing bytecode size.
     *
     * The return values are:
     *  @return balances - The current upscaled token balances (not including BPT)
     *  @return virtualSupply - The Pool's virtual supply
     *  @return protocolFeeAmount - The amount of unpaid protocol fees in BPT
     *  @return lastJoinExitAmp - The Pool's amplification factor at the last join or exit operation
     *  @return currentInvariantWithLastJoinExitAmp - The invariant of the current balances, calculated using the
     *  amplification factor at the last join or exit operation.
     */
    function _getSupplyAndFeesData()
        private
        view
        returns (
            uint256[] memory balances,
            uint256 virtualSupply,
            uint256 protocolFeeAmount,
            uint256 lastJoinExitAmp,
            uint256 currentInvariantWithLastJoinExitAmp
        )
    {
        // First we query the Vault for current registered balances (which includes preminted BPT), to then calculate
        // the current scaled balances and virtual supply.
        (, uint256[] memory registeredBalances, ) = getVault().getPoolTokens(getPoolId());
        _upscaleArray(registeredBalances, _scalingFactors());
        (virtualSupply, balances) = _dropBptItemFromBalances(registeredBalances);

        // Now we need to calculate any BPT due in the form of protocol fees. This requires data from the last join or
        // exit operation. `lastJoinExitAmp` can be useful in the scenario in which the amplification factor has not
        // changed, meaning this old value is equal to the current value.
        uint256 lastPostJoinExitInvariant;
        (lastJoinExitAmp, lastPostJoinExitInvariant) = getLastJoinExitData();

        // Computing the protocol ownership percentage also yields the invariant using the old amplification factor. If
        // it has not changed, then this is also the current invariant.
        uint256 expectedProtocolOwnershipPercentage;
        (
            expectedProtocolOwnershipPercentage,
            currentInvariantWithLastJoinExitAmp
        ) = _getProtocolPoolOwnershipPercentage(balances, lastJoinExitAmp, lastPostJoinExitInvariant);

        protocolFeeAmount = ProtocolFees.bptForPoolOwnershipPercentage(
            virtualSupply,
            expectedProtocolOwnershipPercentage
        );
    }

    /**
     * @dev This function returns the appreciation of BPT relative to the underlying tokens, as an 18 decimal fixed
     * point number. It is simply the ratio of the invariant to the BPT supply.
     *
     * The total supply is initialized to equal the invariant, so this value starts at one. During Pool operation the
     * invariant always grows and shrinks either proportionally to the total supply (in scenarios with no price impact,
     * e.g. proportional joins), or grows faster and shrinks more slowly than it (whenever swap fees are collected or
     * the token rates increase). Therefore, the rate is a monotonically increasing function.
     *
     * WARNING: since this function reads balances directly from the Vault, it is potentially subject to manipulation
     * via reentrancy if called within a Vault context (i.e. in the middle of a join or an exit). It is up to the
     * caller to ensure that the function is safe to call.
     *
     * This may happen e.g. if one of the tokens in the Pool contains some form of callback behavior in the
     * `transferFrom` function (like ERC777 tokens do). These tokens are strictly incompatible with the
     * Vault and Pool design, and are not safe to be used.
     *
     * There are also other situations where calling this function is unsafe. See
     * https://forum.balancer.fi/t/reentrancy-vulnerability-scope-expanded/4345 for reference.
     *
     * To call this function safely, attempt to trigger the reentrancy guard in the Vault by calling a non-reentrant
     * function before calling `getRate`. That will make the transaction revert in an unsafe context.
     * (See `whenNotInVaultContext` in `ComposableStablePoolRates`).
     */
    function getRate() external view virtual override returns (uint256) {
        // We need to compute the current invariant and actual total supply. The latter includes protocol fees that have
        // accrued but are not yet minted: in calculating these we'll actually end up fetching most of the data we need
        // for the invariant.

        (
            uint256[] memory balances,
            uint256 virtualSupply,
            uint256 protocolFeeAmount,
            uint256 lastJoinExitAmp,
            uint256 currentInvariantWithLastJoinExitAmp
        ) = _getSupplyAndFeesData();

        // Due protocol fees will be minted at the next join or exit, so we can simply add them to the current virtual
        // supply to get the actual supply.
        uint256 actualTotalSupply = virtualSupply.add(protocolFeeAmount);

        // All that's missing now is the invariant. We have the balances required to calculate it already, but still
        // need the current amplification factor.
        (uint256 currentAmp, ) = _getAmplificationParameter();

        // It turns out that the process for due protocol fee calculation involves computing the current invariant,
        // except using the amplification factor at the last join or exit. This would typically not be terribly useful,
        // but since the amplification factor only changes rarely there is high probability of its current value being
        // the same as it was in the last join or exit. If that is the case, then we can skip the costly invariant
        // computation altogether.
        uint256 currentInvariant = (currentAmp == lastJoinExitAmp)
            ? currentInvariantWithLastJoinExitAmp
            : StableMath._calculateInvariant(currentAmp, balances);

        // With the current invariant and actual total supply, we can compute the rate as a fixed-point number.
        return currentInvariant.divDown(actualTotalSupply);
    }

    /**
     * @dev Returns the effective BPT supply.
     *
     * In other pools, this would be the same as `totalSupply`, but there are two key differences here:
     *  - this pool pre-mints BPT and holds it in the Vault as a token, and as such we need to subtract the Vault's
     *    balance to get the total "circulating supply". This is called the 'virtualSupply'.
     *  - the Pool owes debt to the Protocol in the form of unminted BPT, which will be minted immediately before the
     *    next join or exit. We need to take these into account since, even if they don't yet exist, they will
     *    effectively be included in any Pool operation that involves BPT.
     *
     * In the vast majority of cases, this function should be used instead of `totalSupply()`.
     *
     * **IMPORTANT NOTE**: calling this function within a Vault context (i.e. in the middle of a join or an exit) is
     * potentially unsafe, since the returned value is manipulable. It is up to the caller to ensure safety.
     *
     * This is because this function calculates the invariant, which requires the state of the pool to be in sync
     * with the state of the Vault. That condition may not be true in the middle of a join or an exit.
     *
     * To call this function safely, attempt to trigger the reentrancy guard in the Vault by calling a non-reentrant
     * function before calling `getActualSupply`. That will make the transaction revert in an unsafe context.
     * (See `whenNotInVaultContext` in `ComposableStablePoolRates`).
     *
     * See https://forum.balancer.fi/t/reentrancy-vulnerability-scope-expanded/4345 for reference.
     */
    function getActualSupply() external view returns (uint256) {
        (, uint256 virtualSupply, uint256 protocolFeeAmount, , ) = _getSupplyAndFeesData();
        return virtualSupply.add(protocolFeeAmount);
    }

    /**
     * @dev This function will revert when called within a Vault context (i.e. in the middle of a join or an exit).
     *
     * This function depends on the invariant value, which may be calculated incorrectly in the middle of a join or
     * an exit, because the state of the pool could be out of sync with the state of the Vault. The modifier
     * `whenNotInVaultContext` prevents calling this function (and in turn, the external
     * `updateProtocolFeePercentageCache`) in such a context.
     *
     * See https://forum.balancer.fi/t/reentrancy-vulnerability-scope-expanded/4345 for reference.
     */
    function _beforeProtocolFeeCacheUpdate() internal override whenNotInVaultContext {
        // The `getRate()` function depends on the actual supply, which in turn depends on the cached protocol fee
        // percentages. Changing these would therefore result in the rate changing, which is not acceptable as this is a
        // sensitive value.
        // Because of this, we pay any due protocol fees *before* updating the cache, making it so that the new
        // percentages only affect future operation of the Pool, and not past fees. As a result, `getRate()` is
        // unaffected by the cached protocol fee percentages changing.

        // Given that this operation is state-changing and relatively complex, we only allow it as long as the Pool is
        // not paused.
        _ensureNotPaused();

        // We need to calculate the amount of unminted BPT that represents protocol fees to then pay those. This yields
        // some auxiliary values that turn out to also be useful for the rest of the tasks we want to perform.
        (
            uint256[] memory balances,
            ,
            uint256 protocolFeeAmount,
            uint256 lastJoinExitAmp,
            uint256 currentInvariantWithLastJoinExitAmp
        ) = _getSupplyAndFeesData();

        if (protocolFeeAmount > 0) {
            _payProtocolFees(protocolFeeAmount);
        }

        // With the fees paid, we now need to calculate the current invariant so we can store it alongside the current
        // amplification factor, marking the Pool as free of protocol debt.
        (uint256 currentAmp, ) = _getAmplificationParameter();

        // It turns out that the process for due protocol fee calculation involves computing the current invariant,
        // except using the amplification factor at the last join or exit. This would typically not be terribly useful,
        // but since the amplification factor only changes rarely there is high probability of its current value being
        // the same as it was in the last join or exit. If that is the case, then we can skip the costly invariant
        // computation altogether.
        uint256 currentInvariant = (currentAmp == lastJoinExitAmp)
            ? currentInvariantWithLastJoinExitAmp
            : StableMath._calculateInvariant(currentAmp, balances);

        _updatePostJoinExit(currentAmp, currentInvariant);
    }

    /**
     * @dev This function will revert when called within a Vault context (i.e. in the middle of a join or an exit).
     *
     * This function depends on the invariant value, which may be calculated incorrectly in the middle of a join or
     * an exit, because the state of the pool could be out of sync with the state of the Vault.
     *
     * The modifier `whenNotInVaultContext` prevents calling this function (and in turn, the external
     * `disableRecoveryMode`) in such a context.
     *
     * See https://forum.balancer.fi/t/reentrancy-vulnerability-scope-expanded/4345 for reference.
     */
    function _onDisableRecoveryMode() internal override whenNotInVaultContext {
        // Enabling recovery mode short-circuits protocol fee computations, forcefully returning a zero percentage,
        // increasing the return value of `getRate()` and effectively forfeiting due protocol fees.

        // Therefore, when exiting recovery mode we store the current invariant and the amplification factor used to
        // compute it, marking the Pool as free of protocol debt. Otherwise it'd be possible for debt to be
        // retroactively accrued, which would be incorrect and could lead to the value of `getRate` decreasing.

        (, uint256[] memory registeredBalances, ) = getVault().getPoolTokens(getPoolId());
        _upscaleArray(registeredBalances, _scalingFactors());
        uint256[] memory balances = _dropBptItem(registeredBalances);

        (uint256 currentAmp, ) = _getAmplificationParameter();
        uint256 currentInvariant = StableMath._calculateInvariant(currentAmp, balances);

        _updatePostJoinExit(currentAmp, currentInvariant);
    }

    // Helpers

    /**
     * @dev Mutates `amounts` by applying `mutation` with each entry in `arguments`.
     *
     * Equivalent to `amounts = amounts.map(mutation)`.
     */
    function _mutateAmounts(
        uint256[] memory toMutate,
        uint256[] memory arguments,
        function(uint256, uint256) pure returns (uint256) mutation
    ) private pure {
        uint256 length = toMutate.length;
        InputHelpers.ensureInputLengthMatch(length, arguments.length);

        for (uint256 i = 0; i < length; ++i) {
            toMutate[i] = mutation(toMutate[i], arguments[i]);
        }
    }

    // Permissioned functions

    /**
     * @dev Inheritance rules still require us to override this in the most derived contract, even though
     * it only calls super.
     */
    function _isOwnerOnlyAction(bytes32 actionId)
        internal
        view
        virtual
        override(
            // Our inheritance pattern creates a small diamond that requires explicitly listing the parents here.
            // Each parent calls the `super` version, so linearization ensures all implementations are called.
            BasePool,
            ComposableStablePoolProtocolFees,
            StablePoolAmplification,
            ComposableStablePoolRates
        )
        returns (bool)
    {
        return super._isOwnerOnlyAction(actionId);
    }
}

// File: @balancer-labs/v2-interfaces/contracts/solidity-utils/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: @balancer-labs/v2-interfaces/contracts/solidity-utils/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: @balancer-labs/v2-interfaces/contracts/solidity-utils/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: @balancer-labs/v2-interfaces/contracts/solidity-utils/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: @balancer-labs/v2-interfaces/contracts/solidity-utils/misc/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 "../openzeppelin/IERC20.sol";

/**
 * @dev Interface for WETH9.
 * See https://github.com/gnosis/canonical-weth/blob/0dd1ea3e295eef916d0c6223ec63141137d22d67/contracts/WETH9.sol
 */
interface IWETH is IERC20 {
    function deposit() external payable;

    function withdraw(uint256 amount) external;
}

// File: @balancer-labs/v2-interfaces/contracts/vault/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: @balancer-labs/v2-interfaces/contracts/vault/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: @balancer-labs/v2-interfaces/contracts/vault/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 "../solidity-utils/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: @balancer-labs/v2-interfaces/contracts/vault/IProtocolFeesCollector.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 "../solidity-utils/openzeppelin/IERC20.sol";

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

interface IProtocolFeesCollector {
    event SwapFeePercentageChanged(uint256 newSwapFeePercentage);
    event FlashLoanFeePercentageChanged(uint256 newFlashLoanFeePercentage);

    function withdrawCollectedFees(
        IERC20[] calldata tokens,
        uint256[] calldata amounts,
        address recipient
    ) external;

    function setSwapFeePercentage(uint256 newSwapFeePercentage) external;

    function setFlashLoanFeePercentage(uint256 newFlashLoanFeePercentage) external;

    function getSwapFeePercentage() external view returns (uint256);

    function getFlashLoanFeePercentage() external view returns (uint256);

    function getCollectedFeeAmounts(IERC20[] memory tokens) external view returns (uint256[] memory feeAmounts);

    function getAuthorizer() external view returns (IAuthorizer);

    function vault() external view returns (IVault);
}

// File: @balancer-labs/v2-interfaces/contracts/standalone-utils/IProtocolFeePercentagesProvider.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;

/**
 * @dev Source of truth for all Protocol Fee percentages, that is, how much the protocol charges certain actions. Some
 * of these values may also be retrievable from other places (such as the swap fee percentage), but this is the
 * preferred source nonetheless.
 */
interface IProtocolFeePercentagesProvider {
    // All fee percentages are 18-decimal fixed point numbers, so e.g. 1e18 = 100% and 1e16 = 1%.

    // Emitted when a new fee type is registered.
    event ProtocolFeeTypeRegistered(uint256 indexed feeType, string name, uint256 maximumPercentage);

    // Emitted when the value of a fee type changes.
    // IMPORTANT: it is possible for a third party to modify the SWAP and FLASH_LOAN fee type values directly in the
    // ProtocolFeesCollector, which will result in this event not being emitted despite their value changing. Such usage
    // of the ProtocolFeesCollector is however discouraged: all state-changing interactions with it should originate in
    // this contract.
    event ProtocolFeePercentageChanged(uint256 indexed feeType, uint256 percentage);

    /**
     * @dev Registers a new fee type in the system, making it queryable via `getFeeTypePercentage` and `getFeeTypeName`,
     * as well as configurable via `setFeeTypePercentage`.
     *
     * `feeType` can be any arbitrary value (that is not in use).
     *
     * It is not possible to de-register fee types, nor change their name or maximum value.
     */
    function registerFeeType(
        uint256 feeType,
        string memory name,
        uint256 maximumValue,
        uint256 initialValue
    ) external;

    /**
     * @dev Returns true if `feeType` has been registered and can be queried.
     */
    function isValidFeeType(uint256 feeType) external view returns (bool);

    /**
     * @dev Returns true if `value` is a valid percentage value for `feeType`.
     */
    function isValidFeeTypePercentage(uint256 feeType, uint256 value) external view returns (bool);

    /**
     * @dev Sets the percentage value for `feeType` to `newValue`.
     *
     * IMPORTANT: it is possible for a third party to modify the SWAP and FLASH_LOAN fee type values directly in the
     * ProtocolFeesCollector, without invoking this function. This will result in the `ProtocolFeePercentageChanged`
     * event not being emitted despite their value changing. Such usage of the ProtocolFeesCollector is however
     * discouraged: only this contract should be granted permission to call `setSwapFeePercentage` and
     * `setFlashLoanFeePercentage`.
     */
    function setFeeTypePercentage(uint256 feeType, uint256 newValue) external;

    /**
     * @dev Returns the current percentage value for `feeType`. This is the preferred mechanism for querying these -
     * whenever possible, use this fucntion instead of e.g. querying the ProtocolFeesCollector.
     */
    function getFeeTypePercentage(uint256 feeType) external view returns (uint256);

    /**
     * @dev Returns `feeType`'s maximum value.
     */
    function getFeeTypeMaximumPercentage(uint256 feeType) external view returns (uint256);

    /**
     * @dev Returns `feeType`'s name.
     */
    function getFeeTypeName(uint256 feeType) external view returns (string memory);
}

library ProtocolFeeType {
    // This list is not exhaustive - more fee types can be added to the system. It is expected for this list to be
    // extended with new fee types as they are registered, to keep them all in one place and reduce
    // likelihood of user error.

    // solhint-disable private-vars-leading-underscore
    uint256 internal constant SWAP = 0;
    uint256 internal constant FLASH_LOAN = 1;
    uint256 internal constant YIELD = 2;
    uint256 internal constant AUM = 3;
    // solhint-enable private-vars-leading-underscore
}

// File: @balancer-labs/v2-interfaces/contracts/solidity-utils/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.
 * Uses the default 'BAL' prefix for the error code
 */
function _require(bool condition, uint256 errorCode) pure {
    if (!condition) _revert(errorCode);
}

/**
 * @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, bytes3 prefix) pure {
    if (!condition) _revert(errorCode, prefix);
}

/**
 * @dev Reverts with a revert reason containing `errorCode`. Only codes up to 999 are supported.
 * Uses the default 'BAL' prefix for the error code
 */
function _revert(uint256 errorCode) pure {
    _revert(errorCode, 0x42414c); // This is the raw byte representation of "BAL"
}

/**
 * @dev Reverts with a revert reason containing `errorCode`. Only codes up to 999 are supported.
 */
function _revert(uint256 errorCode, bytes3 prefix) pure {
    uint256 prefixUint = uint256(uint24(prefix));
    // 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.
        // We first append the '#' character (0x23) to the prefix. In the case of 'BAL', it results in 0x42414c23 ('BAL#')
        // Then, we 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 formattedPrefix := shl(24, add(0x23, shl(8, prefixUint)))

        let revertReason := shl(200, add(formattedPrefix, 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;
    uint256 internal constant NOT_TWO_TOKENS = 210;
    uint256 internal constant DISABLED = 211;

    // 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;
    uint256 internal constant AMP_END_TIME_TOO_CLOSE = 317;
    uint256 internal constant AMP_ONGOING_UPDATE = 318;
    uint256 internal constant AMP_RATE_TOO_HIGH = 319;
    uint256 internal constant AMP_NO_ONGOING_UPDATE = 320;
    uint256 internal constant STABLE_INVARIANT_DIDNT_CONVERGE = 321;
    uint256 internal constant STABLE_GET_BALANCE_DIDNT_CONVERGE = 322;
    uint256 internal constant RELAYER_NOT_CONTRACT = 323;
    uint256 internal constant BASE_POOL_RELAYER_NOT_CALLED = 324;
    uint256 internal constant REBALANCING_RELAYER_REENTERED = 325;
    uint256 internal constant GRADUAL_UPDATE_TIME_TRAVEL = 326;
    uint256 internal constant SWAPS_DISABLED = 327;
    uint256 internal constant CALLER_IS_NOT_LBP_OWNER = 328;
    uint256 internal constant PRICE_RATE_OVERFLOW = 329;
    uint256 internal constant INVALID_JOIN_EXIT_KIND_WHILE_SWAPS_DISABLED = 330;
    uint256 internal constant WEIGHT_CHANGE_TOO_FAST = 331;
    uint256 internal constant LOWER_GREATER_THAN_UPPER_TARGET = 332;
    uint256 internal constant UPPER_TARGET_TOO_HIGH = 333;
    uint256 internal constant UNHANDLED_BY_LINEAR_POOL = 334;
    uint256 internal constant OUT_OF_TARGET_RANGE = 335;
    uint256 internal constant UNHANDLED_EXIT_KIND = 336;
    uint256 internal constant UNAUTHORIZED_EXIT = 337;
    uint256 internal constant MAX_MANAGEMENT_SWAP_FEE_PERCENTAGE = 338;
    uint256 internal constant UNHANDLED_BY_MANAGED_POOL = 339;
    uint256 internal constant UNHANDLED_BY_PHANTOM_POOL = 340;
    uint256 internal constant TOKEN_DOES_NOT_HAVE_RATE_PROVIDER = 341;
    uint256 internal constant INVALID_INITIALIZATION = 342;
    uint256 internal constant OUT_OF_NEW_TARGET_RANGE = 343;
    uint256 internal constant FEATURE_DISABLED = 344;
    uint256 internal constant UNINITIALIZED_POOL_CONTROLLER = 345;
    uint256 internal constant SET_SWAP_FEE_DURING_FEE_CHANGE = 346;
    uint256 internal constant SET_SWAP_FEE_PENDING_FEE_CHANGE = 347;
    uint256 internal constant CHANGE_TOKENS_DURING_WEIGHT_CHANGE = 348;
    uint256 internal constant CHANGE_TOKENS_PENDING_WEIGHT_CHANGE = 349;
    uint256 internal constant MAX_WEIGHT = 350;
    uint256 internal constant UNAUTHORIZED_JOIN = 351;
    uint256 internal constant MAX_MANAGEMENT_AUM_FEE_PERCENTAGE = 352;
    uint256 internal constant FRACTIONAL_TARGET = 353;

    // 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;
    uint256 internal constant CALLER_IS_NOT_OWNER = 426;
    uint256 internal constant NEW_OWNER_IS_ZERO = 427;
    uint256 internal constant CODE_DEPLOYMENT_FAILED = 428;
    uint256 internal constant CALL_TO_NON_CONTRACT = 429;
    uint256 internal constant LOW_LEVEL_CALL_FAILED = 430;
    uint256 internal constant NOT_PAUSED = 431;
    uint256 internal constant ADDRESS_ALREADY_ALLOWLISTED = 432;
    uint256 internal constant ADDRESS_NOT_ALLOWLISTED = 433;
    uint256 internal constant ERC20_BURN_EXCEEDS_BALANCE = 434;
    uint256 internal constant INVALID_OPERATION = 435;
    uint256 internal constant CODEC_OVERFLOW = 436;
    uint256 internal constant IN_RECOVERY_MODE = 437;
    uint256 internal constant NOT_IN_RECOVERY_MODE = 438;
    uint256 internal constant INDUCED_FAILURE = 439;
    uint256 internal constant EXPIRED_SIGNATURE = 440;
    uint256 internal constant MALFORMED_SIGNATURE = 441;
    uint256 internal constant SAFE_CAST_VALUE_CANT_FIT_UINT64 = 442;
    uint256 internal constant UNHANDLED_FEE_TYPE = 443;

    // 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;
    uint256 internal constant AUM_FEE_PERCENTAGE_TOO_HIGH = 603;

    // Misc
    uint256 internal constant UNIMPLEMENTED = 998;
    uint256 internal constant SHOULD_NOT_HAPPEN = 999;
}

// File: @balancer-labs/v2-solidity-utils/contracts/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 "@balancer-labs/v2-interfaces/contracts/solidity-utils/helpers/BalancerErrors.sol";
import "@balancer-labs/v2-interfaces/contracts/solidity-utils/helpers/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: @balancer-labs/v2-interfaces/contracts/pool-stable/StablePoolUserData.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;

library StablePoolUserData {
    enum JoinKind { INIT, EXACT_TOKENS_IN_FOR_BPT_OUT, TOKEN_IN_FOR_EXACT_BPT_OUT, ALL_TOKENS_IN_FOR_EXACT_BPT_OUT }
    enum ExitKind { EXACT_BPT_IN_FOR_ONE_TOKEN_OUT, BPT_IN_FOR_EXACT_TOKENS_OUT, EXACT_BPT_IN_FOR_ALL_TOKENS_OUT }

    function joinKind(bytes memory self) internal pure returns (JoinKind) {
        return abi.decode(self, (JoinKind));
    }

    function exitKind(bytes memory self) internal pure returns (ExitKind) {
        return abi.decode(self, (ExitKind));
    }

    // Joins

    function initialAmountsIn(bytes memory self) internal pure returns (uint256[] memory amountsIn) {
        (, amountsIn) = abi.decode(self, (JoinKind, uint256[]));
    }

    function exactTokensInForBptOut(bytes memory self)
        internal
        pure
        returns (uint256[] memory amountsIn, uint256 minBPTAmountOut)
    {
        (, amountsIn, minBPTAmountOut) = abi.decode(self, (JoinKind, uint256[], uint256));
    }

    function tokenInForExactBptOut(bytes memory self) internal pure returns (uint256 bptAmountOut, uint256 tokenIndex) {
        (, bptAmountOut, tokenIndex) = abi.decode(self, (JoinKind, uint256, uint256));
    }

    function allTokensInForExactBptOut(bytes memory self) internal pure returns (uint256 bptAmountOut) {
        (, bptAmountOut) = abi.decode(self, (JoinKind, uint256));
    }

    // Exits

    function exactBptInForTokenOut(bytes memory self) internal pure returns (uint256 bptAmountIn, uint256 tokenIndex) {
        (, bptAmountIn, tokenIndex) = abi.decode(self, (ExitKind, uint256, uint256));
    }

    function exactBptInForTokensOut(bytes memory self) internal pure returns (uint256 bptAmountIn) {
        (, bptAmountIn) = abi.decode(self, (ExitKind, uint256));
    }

    function bptInForExactTokensOut(bytes memory self)
        internal
        pure
        returns (uint256[] memory amountsOut, uint256 maxBPTAmountIn)
    {
        (, amountsOut, maxBPTAmountIn) = abi.decode(self, (ExitKind, uint256[], uint256));
    }
}

// File: @balancer-labs/v2-interfaces/contracts/pool-utils/IRateProvider.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 IRateProvider {
    /**
     * @dev Returns an 18 decimal fixed point number that is the exchange rate of the token to some other underlying
     * token. The meaning of this rate depends on the context.
     */
    function getRate() external view returns (uint256);
}

// File: @balancer-labs/v2-solidity-utils/contracts/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 "@balancer-labs/v2-interfaces/contracts/solidity-utils/helpers/BalancerErrors.sol";

import "./LogExpMath.sol";

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

library FixedPoint {
    uint256 internal constant ONE = 1e18; // 18 decimal places
    uint256 internal constant TWO = 2 * ONE;
    uint256 internal constant FOUR = 4 * ONE;
    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) {
        // Optimize for when y equals 1.0, 2.0 or 4.0, as those are very simple to implement and occur often in 50/50
        // and 80/20 Weighted Pools
        if (y == ONE) {
            return x;
        } else if (y == TWO) {
            return mulDown(x, x);
        } else if (y == FOUR) {
            uint256 square = mulDown(x, x);
            return mulDown(square, square);
        } else {
            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) {
        // Optimize for when y equals 1.0, 2.0 or 4.0, as those are very simple to implement and occur often in 50/50
        // and 80/20 Weighted Pools
        if (y == ONE) {
            return x;
        } else if (y == TWO) {
            return mulUp(x, x);
        } else if (y == FOUR) {
            uint256 square = mulUp(x, x);
            return mulUp(square, square);
        } else {
            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: @balancer-labs/v2-solidity-utils/contracts/math/Math.sol



// SPDX-License-Identifier: MIT

pragma solidity ^0.7.0;

import "@balancer-labs/v2-interfaces/contracts/solidity-utils/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 absolute value of a signed integer.
     */
    function abs(int256 a) internal pure returns (uint256) {
        return a > 0 ? uint256(a) : uint256(-a);
    }

    /**
     * @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 div(
        uint256 a,
        uint256 b,
        bool roundUp
    ) internal pure returns (uint256) {
        return roundUp ? divUp(a, b) : divDown(a, b);
    }

    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: @balancer-labs/v2-solidity-utils/contracts/helpers/ERC20Helpers.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 "@balancer-labs/v2-interfaces/contracts/solidity-utils/helpers/BalancerErrors.sol";
import "@balancer-labs/v2-interfaces/contracts/solidity-utils/openzeppelin/IERC20.sol";
import "@balancer-labs/v2-interfaces/contracts/vault/IAsset.sol";

// solhint-disable

function _asIAsset(IERC20[] memory tokens) pure returns (IAsset[] memory assets) {
    // solhint-disable-next-line no-inline-assembly
    assembly {
        assets := tokens
    }
}

function _sortTokens(
    IERC20 tokenA,
    IERC20 tokenB,
    IERC20 tokenC
) pure returns (IERC20[] memory tokens) {
    (uint256 indexTokenA, uint256 indexTokenB, uint256 indexTokenC) = _getSortedTokenIndexes(tokenA, tokenB, tokenC);
    tokens = new IERC20[](3);
    tokens[indexTokenA] = tokenA;
    tokens[indexTokenB] = tokenB;
    tokens[indexTokenC] = tokenC;
}

function _insertSorted(IERC20[] memory tokens, IERC20 token) pure returns (IERC20[] memory sorted) {
    sorted = new IERC20[](tokens.length + 1);

    if (tokens.length == 0) {
        sorted[0] = token;
        return sorted;
    }

    uint256 i;
    for (i = tokens.length; i > 0 && tokens[i - 1] > token; i--) sorted[i] = tokens[i - 1];
    for (uint256 j = 0; j < i; j++) sorted[j] = tokens[j];
    sorted[i] = token;
}

function _appendToken(IERC20[] memory tokens, IERC20 newToken) pure returns (IERC20[] memory newTokens) {
    uint256 numTokens = tokens.length;
    newTokens = new IERC20[](numTokens + 1);

    for (uint256 i = 0; i < numTokens; ++i) newTokens[i] = tokens[i];
    newTokens[numTokens] = newToken;
}

function _findTokenIndex(IERC20[] memory tokens, IERC20 token) pure returns (uint256) {
    // Note that while we know tokens are initially sorted, we cannot assume this will hold throughout
    // the pool's lifetime, as pools with mutable tokens can append and remove tokens in any order.
    uint256 tokensLength = tokens.length;
    for (uint256 i = 0; i < tokensLength; i++) {
        if (tokens[i] == token) {
            return i;
        }
    }

    _revert(Errors.INVALID_TOKEN);
}

function _getSortedTokenIndexes(
    IERC20 tokenA,
    IERC20 tokenB,
    IERC20 tokenC
)
    pure
    returns (
        uint256 indexTokenA,
        uint256 indexTokenB,
        uint256 indexTokenC
    )
{
    if (tokenA < tokenB) {
        if (tokenB < tokenC) {
            // (tokenA, tokenB, tokenC)
            return (0, 1, 2);
        } else if (tokenA < tokenC) {
            // (tokenA, tokenC, tokenB)
            return (0, 2, 1);
        } else {
            // (tokenC, tokenA, tokenB)
            return (1, 2, 0);
        }
    } else {
        // tokenB < tokenA
        if (tokenC < tokenB) {
            // (tokenC, tokenB, tokenA)
            return (2, 1, 0);
        } else if (tokenC < tokenA) {
            // (tokenB, tokenC, tokenA)
            return (2, 0, 1);
        } else {
            // (tokenB, tokenA, tokenC)
            return (1, 0, 2);
        }
    }
}

// File: @balancer-labs/v2-solidity-utils/contracts/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 "@balancer-labs/v2-interfaces/contracts/solidity-utils/openzeppelin/IERC20.sol";
import "@balancer-labs/v2-interfaces/contracts/solidity-utils/helpers/BalancerErrors.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(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: @balancer-labs/v2-pool-utils/contracts/BaseGeneralPool.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 "@balancer-labs/v2-interfaces/contracts/vault/IGeneralPool.sol";

import "./BasePool.sol";

/**
 * @dev Extension of `BasePool`, adding a handler for `IGeneralPool.onSwap`.
 *
 * Derived contracts must call `BasePool`'s constructor, and implement `_onSwapGivenIn` and `_onSwapGivenOut` along with
 * `BasePool`'s virtual functions. Inheriting from this contract lets derived contracts choose the General
 * specialization setting.
 */
abstract contract BaseGeneralPool is IGeneralPool, BasePool {
    // Swap Hooks

    function onSwap(
        SwapRequest memory swapRequest,
        uint256[] memory balances,
        uint256 indexIn,
        uint256 indexOut
    ) external override onlyVault(swapRequest.poolId) returns (uint256) {
        _beforeSwapJoinExit();

        _validateIndexes(indexIn, indexOut, _getTotalTokens());
        uint256[] memory scalingFactors = _scalingFactors();

        return
            swapRequest.kind == IVault.SwapKind.GIVEN_IN
                ? _swapGivenIn(swapRequest, balances, indexIn, indexOut, scalingFactors)
                : _swapGivenOut(swapRequest, balances, indexIn, indexOut, scalingFactors);
    }

    function _swapGivenIn(
        SwapRequest memory swapRequest,
        uint256[] memory balances,
        uint256 indexIn,
        uint256 indexOut,
        uint256[] memory scalingFactors
    ) internal virtual returns (uint256) {
        // Fees are subtracted before scaling, to reduce the complexity of the rounding direction analysis.
        swapRequest.amount = _subtractSwapFeeAmount(swapRequest.amount);

        _upscaleArray(balances, scalingFactors);
        swapRequest.amount = _upscale(swapRequest.amount, scalingFactors[indexIn]);

        uint256 amountOut = _onSwapGivenIn(swapRequest, balances, indexIn, indexOut);

        // amountOut tokens are exiting the Pool, so we round down.
        return _downscaleDown(amountOut, scalingFactors[indexOut]);
    }

    function _swapGivenOut(
        SwapRequest memory swapRequest,
        uint256[] memory balances,
        uint256 indexIn,
        uint256 indexOut,
        uint256[] memory scalingFactors
    ) internal virtual returns (uint256) {
        _upscaleArray(balances, scalingFactors);
        swapRequest.amount = _upscale(swapRequest.amount, scalingFactors[indexOut]);

        uint256 amountIn = _onSwapGivenOut(swapRequest, balances, indexIn, indexOut);

        // amountIn tokens are entering the Pool, so we round up.
        amountIn = _downscaleUp(amountIn, scalingFactors[indexIn]);

        // Fees are added after scaling happens, to reduce the complexity of the rounding direction analysis.
        return _addSwapFeeAmount(amountIn);
    }

    /*
     * @dev Called when a swap with the Pool occurs, where the amount of tokens entering the Pool is known.
     *
     * Returns the amount of tokens that will be taken from the Pool in return.
     *
     * All amounts inside `swapRequest` and `balances` are upscaled. The swap fee has already been deducted from
     * `swapRequest.amount`.
     *
     * The return value is also considered upscaled, and will be downscaled (rounding down) before returning it to the
     * Vault.
     */
    function _onSwapGivenIn(
        SwapRequest memory swapRequest,
        uint256[] memory balances,
        uint256 indexIn,
        uint256 indexOut
    ) internal virtual returns (uint256);

    /*
     * @dev Called when a swap with the Pool occurs, where the amount of tokens exiting the Pool is known.
     *
     * Returns the amount of tokens that will be granted to the Pool in return.
     *
     * All amounts inside `swapRequest` and `balances` are upscaled.
     *
     * The return value is also considered upscaled, and will be downscaled (rounding up) before applying the swap fee
     * and returning it to the Vault.
     */
    function _onSwapGivenOut(
        SwapRequest memory swapRequest,
        uint256[] memory balances,
        uint256 indexIn,
        uint256 indexOut
    ) internal virtual returns (uint256);

    function _validateIndexes(
        uint256 indexIn,
        uint256 indexOut,
        uint256 limit
    ) private pure {
        _require(indexIn < limit && indexOut < limit, Errors.OUT_OF_BOUNDS);
    }
}

// File: @balancer-labs/v2-pool-utils/contracts/rates/PriceRateCache.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 "@balancer-labs/v2-interfaces/contracts/solidity-utils/helpers/BalancerErrors.sol";

import "@balancer-labs/v2-solidity-utils/contracts/helpers/WordCodec.sol";

/**
 * Price rate caches are used to avoid querying the price rate for a token every time we need to work with it. It is
 * useful for slow changing rates, such as those that arise from interest-bearing tokens (e.g. waDAI into DAI).
 *
 * The cache data is packed into a single bytes32 value with the following structure:
 * [ 32 bits |  32 bits  |  96 bits  |    96 bits    ]
 * [ expires | duration  | old rate  | current rate  ]
 * |MSB                                           LSB|
 *
 * 'rate' is an 18 decimal fixed point number, supporting rates of up to ~3e10. 'expires' is a Unix timestamp, and
 * 'duration' is expressed in seconds.
 */
library PriceRateCache {
    using WordCodec for bytes32;

    uint256 private constant _CURRENT_PRICE_RATE_OFFSET = 0;
    uint256 private constant _OLD_PRICE_RATE_OFFSET = 96;
    uint256 private constant _PRICE_RATE_CACHE_DURATION_OFFSET = 192;
    uint256 private constant _PRICE_RATE_CACHE_EXPIRES_OFFSET = 224;

    uint256 private constant _RATE_BIT_LENGTH = 96;
    uint256 private constant _DURATION_BIT_LENGTH = 32;

    /**
     * @dev Returns the current rate in the price rate cache.
     */
    function getCurrentRate(bytes32 cache) internal pure returns (uint256) {
        return cache.decodeUint(_CURRENT_PRICE_RATE_OFFSET, _RATE_BIT_LENGTH);
    }

    /**
     * @dev Returns the old rate in the price rate cache.
     */
    function getOldRate(bytes32 cache) internal pure returns (uint256) {
        return cache.decodeUint(_OLD_PRICE_RATE_OFFSET, _RATE_BIT_LENGTH);
    }

    /**
     * @dev Copies the current rate to the old rate.
     */
    function updateOldRate(bytes32 cache) internal pure returns (bytes32) {
        return cache.insertUint(getCurrentRate(cache), _OLD_PRICE_RATE_OFFSET, _RATE_BIT_LENGTH);
    }

    /**
     * @dev Returns the duration of a price rate cache.
     */
    function getDuration(bytes32 cache) internal pure returns (uint256) {
        return cache.decodeUint(_PRICE_RATE_CACHE_DURATION_OFFSET, _DURATION_BIT_LENGTH);
    }

    /**
     * @dev Returns the duration and expiration time of a price rate cache.
     */
    function getTimestamps(bytes32 cache) internal pure returns (uint256 duration, uint256 expires) {
        duration = getDuration(cache);
        expires = cache.decodeUint(_PRICE_RATE_CACHE_EXPIRES_OFFSET, _DURATION_BIT_LENGTH);
    }

    /**
     * @dev Encodes rate and duration into a price rate cache. The expiration time is computed automatically, counting
     * from the current time.
     */
    function updateRateAndDuration(
        bytes32 cache,
        uint256 rate,
        uint256 duration
    ) internal view returns (bytes32) {
        _require(rate >> _RATE_BIT_LENGTH == 0, Errors.PRICE_RATE_OVERFLOW);

        // solhint-disable not-rely-on-time
        return
            cache
                .insertUint(rate, _CURRENT_PRICE_RATE_OFFSET, _RATE_BIT_LENGTH)
                .insertUint(duration, _PRICE_RATE_CACHE_DURATION_OFFSET, _DURATION_BIT_LENGTH)
                .insertUint(block.timestamp + duration, _PRICE_RATE_CACHE_EXPIRES_OFFSET, _DURATION_BIT_LENGTH);
    }

    /**
     * @dev Update the current rate in a price rate cache.
     */
    function updateCurrentRate(bytes32 cache, uint256 rate) internal pure returns (bytes32) {
        _require(rate >> _RATE_BIT_LENGTH == 0, Errors.PRICE_RATE_OVERFLOW);

        return cache.insertUint(rate, _CURRENT_PRICE_RATE_OFFSET, _RATE_BIT_LENGTH);
    }

    /**
     * @dev Update the duration (and expiration) in a price rate cache.
     */
    function updateDuration(bytes32 cache, uint256 duration) internal view returns (bytes32) {
        return
            cache.insertUint(duration, _PRICE_RATE_CACHE_DURATION_OFFSET, _DURATION_BIT_LENGTH).insertUint(
                block.timestamp + duration,
                _PRICE_RATE_CACHE_EXPIRES_OFFSET,
                _DURATION_BIT_LENGTH
            );
    }

    /**
     * @dev Returns rate, duration and expiration time of a price rate cache.
     */
    function decode(bytes32 cache)
        internal
        pure
        returns (
            uint256 rate,
            uint256 duration,
            uint256 expires
        )
    {
        rate = getCurrentRate(cache);
        (duration, expires) = getTimestamps(cache);
    }
}

// File: contracts/ComposableStablePoolStorage.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 "@balancer-labs/v2-interfaces/contracts/solidity-utils/helpers/BalancerErrors.sol";
import "@balancer-labs/v2-interfaces/contracts/solidity-utils/openzeppelin/IERC20.sol";
import "@balancer-labs/v2-interfaces/contracts/pool-utils/IRateProvider.sol";

import "@balancer-labs/v2-pool-utils/contracts/BasePool.sol";

import "./StableMath.sol";

abstract contract ComposableStablePoolStorage is BasePool {
    using FixedPoint for uint256;
    using WordCodec for bytes32;

    struct StorageParams {
        IERC20[] registeredTokens;
        IRateProvider[] tokenRateProviders;
        bool exemptFromYieldProtocolFeeFlag;
    }

    // This minimum refers not to the total tokens, but rather to the non-BPT tokens. The minimum value for _totalTokens
    // is therefore _MIN_NON_BPT_TOKENS + 1.
    uint256 private constant _MIN_NON_BPT_TOKENS = 2;

    // The Pool will register n+1 tokens, where n are the actual tokens in the Pool, and the other one is the BPT
    // itself.
    uint256 private immutable _totalTokens;

    // The index of BPT in the tokens and balances arrays, i.e. its index when calling IVault.registerTokens().
    uint256 private immutable _bptIndex;

    // These are the registered tokens: one of them will be the BPT.
    IERC20 private immutable _token0;
    IERC20 private immutable _token1;
    IERC20 private immutable _token2;
    IERC20 private immutable _token3;
    IERC20 private immutable _token4;
    IERC20 private immutable _token5;

    // All token balances are normalized to behave as if the token had 18 decimals. We assume a token's decimals will
    // not change throughout its lifetime, and store the corresponding scaling factor for each at construction time.
    // These factors are always greater than or equal to one: tokens with more than 18 decimals are not supported.

    uint256 internal immutable _scalingFactor0;
    uint256 internal immutable _scalingFactor1;
    uint256 internal immutable _scalingFactor2;
    uint256 internal immutable _scalingFactor3;
    uint256 internal immutable _scalingFactor4;
    uint256 internal immutable _scalingFactor5;

    // Rate Providers accommodate tokens with a known price ratio, such as Compound's cTokens.

    IRateProvider internal immutable _rateProvider0;
    IRateProvider internal immutable _rateProvider1;
    IRateProvider internal immutable _rateProvider2;
    IRateProvider internal immutable _rateProvider3;
    IRateProvider internal immutable _rateProvider4;
    IRateProvider internal immutable _rateProvider5;

    // This is a bitmap which allows querying whether a token at a particular index:
    // - has a rate provider associated with it.
    // - is exempt from yield protocol fees.
    // This is required as the data stored in this bitmap is computed from values in immutable storage,
    // without this bitmap we would have to manually search through token by token to reach these values.
    // The data structure is as follows:
    //
    // [  unused  | rate provider flags | exemption flags ]
    // [ 244 bits |        6 bits       |     6 bits      ]
    bytes32 private immutable _rateProviderInfoBitmap;

    // Indicates whether all the tokens from the pool are exempt from yield protocol fee or not.
    bool private immutable _exemptFromYieldProtocolFee;

    uint256 private constant _RATE_PROVIDER_FLAGS_OFFSET = 6;

    constructor(StorageParams memory params) {
        // BasePool checks that the Pool has at least two tokens, but since one of them is the BPT (this contract), we
        // need to check ourselves that there are at least creator-supplied tokens (i.e. the minimum number of total
        // tokens for this contract is actually three, including the BPT).
        uint256 totalTokens = params.registeredTokens.length;
        _require(totalTokens > _MIN_NON_BPT_TOKENS, Errors.MIN_TOKENS);
        InputHelpers.ensureInputLengthMatch(totalTokens - 1, params.tokenRateProviders.length);

        _totalTokens = totalTokens;

        // Immutable variables cannot be initialized inside an if statement, so we must do conditional assignments
        _token0 = params.registeredTokens[0];
        _token1 = params.registeredTokens[1];
        _token2 = params.registeredTokens[2];
        _token3 = totalTokens > 3 ? params.registeredTokens[3] : IERC20(0);
        _token4 = totalTokens > 4 ? params.registeredTokens[4] : IERC20(0);
        _token5 = totalTokens > 5 ? params.registeredTokens[5] : IERC20(0);

        _scalingFactor0 = _computeScalingFactor(params.registeredTokens[0]);
        _scalingFactor1 = _computeScalingFactor(params.registeredTokens[1]);
        _scalingFactor2 = _computeScalingFactor(params.registeredTokens[2]);
        _scalingFactor3 = totalTokens > 3 ? _computeScalingFactor(params.registeredTokens[3]) : 0;
        _scalingFactor4 = totalTokens > 4 ? _computeScalingFactor(params.registeredTokens[4]) : 0;
        _scalingFactor5 = totalTokens > 5 ? _computeScalingFactor(params.registeredTokens[5]) : 0;

        // The Vault keeps track of all Pool tokens in a specific order: we need to know what the index of BPT is in
        // this ordering to be able to identify it when balances arrays are received. Since the tokens array is sorted,
        // we need to find the correct BPT index in the array returned by `_insertSorted()`.
        // See `IVault.getPoolTokens()` for more information regarding token ordering.
        uint256 bptIndex;
        for (
            bptIndex = params.registeredTokens.length - 1;
            bptIndex > 0 && params.registeredTokens[bptIndex] > IERC20(this);
            bptIndex--
        ) {
            // solhint-disable-previous-line no-empty-blocks
        }
        _bptIndex = bptIndex;

        // The rate providers are stored as immutable state variables, and for simplicity when accessing those we'll
        // reference them by token index in the full base tokens plus BPT set (i.e. the tokens the Pool registers). Due
        // to immutable variables requiring an explicit assignment instead of defaulting to an empty value, it is
        // simpler to create a new memory array with the values we want to assign to the immutable state variables.
        IRateProvider[] memory rateProviders = new IRateProvider[](params.registeredTokens.length);

        bytes32 rateProviderInfoBitmap;

        // The exemptFromYieldFlag should never be set on a token without a rate provider.
        // This would cause division by zero errors downstream.
        for (uint256 i = 0; i < params.registeredTokens.length; ++i) {
            if (i < bptIndex) {
                rateProviders[i] = params.tokenRateProviders[i];
            } else if (i != bptIndex) {
                rateProviders[i] = params.tokenRateProviders[i - 1];
            } else {
                // do nothing for i == bptIndex
                continue;
            }
            // Store whether token has rate provider
            rateProviderInfoBitmap = rateProviderInfoBitmap.insertBool(
                rateProviders[i] != IRateProvider(0),
                _RATE_PROVIDER_FLAGS_OFFSET + i
            );
            // Store whether token is exempt from yield fees (only with rate providers).
            if (params.exemptFromYieldProtocolFeeFlag && rateProviders[i] != IRateProvider(0)) {
                rateProviderInfoBitmap = rateProviderInfoBitmap.insertBool(true, i);
            }
        }

        // Either all tokens are exempt, or none of them are. This is defined by the input parameter.
        _exemptFromYieldProtocolFee = params.exemptFromYieldProtocolFeeFlag;

        // Immutable variables cannot be initialized inside an if statement, so we must do conditional assignments
        _rateProvider0 = rateProviders[0];
        _rateProvider1 = rateProviders[1];
        _rateProvider2 = rateProviders[2];
        _rateProvider3 = (rateProviders.length > 3) ? rateProviders[3] : IRateProvider(0);
        _rateProvider4 = (rateProviders.length > 4) ? rateProviders[4] : IRateProvider(0);
        _rateProvider5 = (rateProviders.length > 5) ? rateProviders[5] : IRateProvider(0);

        _rateProviderInfoBitmap = rateProviderInfoBitmap;
    }

    // Tokens

    function _getTotalTokens() internal view virtual override returns (uint256) {
        return _totalTokens;
    }

    function _getMaxTokens() internal pure override returns (uint256) {
        // The BPT will be one of the Pool tokens, but it is unaffected by the Stable 5 token limit.
        return StableMath._MAX_STABLE_TOKENS + 1;
    }

    function getBptIndex() public view returns (uint256) {
        return _bptIndex;
    }

    function _getTokenIndex(IERC20 token) internal view returns (uint256) {
        if (token == _token0) return 0;
        if (token == _token1) return 1;
        if (token == _token2) return 2;
        if (token == _token3) return 3;
        if (token == _token4) return 4;
        if (token == _token5) return 5;

        _revert(Errors.INVALID_TOKEN);
    }

    function _scalingFactor(IERC20) internal view virtual override returns (uint256) {
        // We never use a single token's scaling factor by itself, we always process the entire array at once.
        // Therefore we don't bother providing an implementation for this.
        _revert(Errors.UNIMPLEMENTED);
    }

    // Index helpers

    // Convert from an index into an array including BPT (the Vault's registered token list), to an index
    // into an array excluding BPT (usually from user input, such as amountsIn/Out).
    // `index` must not be the BPT token index itself.
    function _skipBptIndex(uint256 index) internal view returns (uint256) {
        // Currently this is never called with an index passed in from user input, so this check
        // should not be necessary. Included for completion (and future proofing).
        _require(index != getBptIndex(), Errors.OUT_OF_BOUNDS);

        return index < getBptIndex() ? index : index.sub(1);
    }

    /**
     * @dev Remove the item at `_bptIndex` from an arbitrary array (e.g., amountsIn).
     */
    function _dropBptItem(uint256[] memory amounts) internal view returns (uint256[] memory) {
        uint256[] memory amountsWithoutBpt = new uint256[](amounts.length - 1);
        for (uint256 i = 0; i < amountsWithoutBpt.length; i++) {
            amountsWithoutBpt[i] = amounts[i < getBptIndex() ? i : i + 1];
        }

        return amountsWithoutBpt;
    }

    /**
     * @dev Same as `_dropBptItem`, except the virtual supply is also returned, and `balances` is assumed to be the
     * current Pool balances (including BPT).
     */
    function _dropBptItemFromBalances(uint256[] memory registeredBalances)
        internal
        view
        returns (uint256, uint256[] memory)
    {
        return (_getVirtualSupply(registeredBalances[getBptIndex()]), _dropBptItem(registeredBalances));
    }

    // Convert from an index into an array excluding BPT (usually from user input, such as amountsIn/Out),
    // to an index into an array including BPT (the Vault's registered token list).
    // `index` must not be the BPT token index itself, if it is the last element, and the result must be
    // in the range of registered tokens.
    function _addBptIndex(uint256 index) internal view returns (uint256 registeredIndex) {
        // This can be called from an index passed in from user input.
        registeredIndex = index < getBptIndex() ? index : index.add(1);

        // TODO: `indexWithBpt != getBptIndex()` follows from above line and so can be removed.
        _require(registeredIndex < _totalTokens && registeredIndex != getBptIndex(), Errors.OUT_OF_BOUNDS);
    }

    /**
     * @dev Take an array of arbitrary values the size of the token set without BPT, and insert the given
     * bptAmount at the bptIndex location.
     *
     * The caller is responsible for ensuring the `amounts` input array is sized properly; this function
     * performs no checks.
     */
    function _addBptItem(uint256[] memory amounts, uint256 bptAmount)
        internal
        view
        returns (uint256[] memory registeredTokenAmounts)
    {
        registeredTokenAmounts = new uint256[](amounts.length + 1);
        for (uint256 i = 0; i < registeredTokenAmounts.length; i++) {
            registeredTokenAmounts[i] = i == getBptIndex() ? bptAmount : amounts[i < getBptIndex() ? i : i - 1];
        }
    }

    // Rate Providers

    function _getScalingFactor(uint256 index) internal view returns (uint256) {
        if (index == 0) return _scalingFactor0;
        if (index == 1) return _scalingFactor1;
        if (index == 2) return _scalingFactor2;
        if (index == 3) return _scalingFactor3;
        if (index == 4) return _scalingFactor4;
        if (index == 5) return _scalingFactor5;
        else {
            _revert(Errors.INVALID_TOKEN);
        }
    }

    /**
     * @dev Returns the rate providers configured for each token (in the same order as registered).
     */
    function getRateProviders() external view returns (IRateProvider[] memory) {
        uint256 totalTokens = _getTotalTokens();
        IRateProvider[] memory providers = new IRateProvider[](totalTokens);

        for (uint256 i = 0; i < totalTokens; ++i) {
            providers[i] = _getRateProvider(i);
        }

        return providers;
    }

    function _getRateProvider(uint256 index) internal view returns (IRateProvider) {
        if (index == 0) return _rateProvider0;
        if (index == 1) return _rateProvider1;
        if (index == 2) return _rateProvider2;
        if (index == 3) return _rateProvider3;
        if (index == 4) return _rateProvider4;
        if (index == 5) return _rateProvider5;
        else {
            _revert(Errors.INVALID_TOKEN);
        }
    }

    /**
     * @notice Return true if the token at this index has a rate provider
     */
    function _hasRateProvider(uint256 tokenIndex) internal view returns (bool) {
        return _rateProviderInfoBitmap.decodeBool(_RATE_PROVIDER_FLAGS_OFFSET + tokenIndex);
    }

    /**
     * @notice Return true if all tokens are exempt from yield fees.
     */
    function isExemptFromYieldProtocolFee() public view returns (bool) {
        return _exemptFromYieldProtocolFee;
    }

    /**
     * @dev Returns whether the token is exempt from protocol fees on the yield.
     * If the BPT token is passed in (which doesn't make much sense, but shouldn't fail,
     * since it is a valid pool token), the corresponding flag will be false.
     */
    function isTokenExemptFromYieldProtocolFee(IERC20 token) external view returns (bool) {
        return _exemptFromYieldProtocolFee && _hasRateProvider(_getTokenIndex(token));
    }

    // Virtual Supply

    /**
     * @dev Returns the number of tokens in circulation.
     *
     * WARNING: in the vast majority of cases this is not a useful value, since it does not include the debt the Pool
     * accrued in the form of unminted BPT for the ProtocolFeesCollector. Look into `getActualSupply()` and how that's
     * different.
     *
     * In other pools, this would be the same as `totalSupply`, but since this pool pre-mints BPT and holds it in the
     * Vault as a token, we need to subtract the Vault's balance to get the total "circulating supply". Both the
     * totalSupply and Vault balance can change. If users join or exit using swaps, some of the preminted BPT are
     * exchanged, so the Vault's balance increases after joins and decreases after exits. If users call the regular
     * joins/exit functions, the totalSupply can change as BPT are minted for joins or burned for exits.
     */
    function _getVirtualSupply(uint256 bptBalance) internal view returns (uint256) {
        // The initial amount of BPT pre-minted is _PREMINTED_TOKEN_BALANCE, and it goes entirely to the pool balance in
        // the vault. So the virtualSupply (the amount of BPT supply in circulation) is defined as:
        // virtualSupply = totalSupply() - _balances[_bptIndex]
        return totalSupply().sub(bptBalance);
    }
}

// File: contracts/ComposableStablePoolRates.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 "@balancer-labs/v2-interfaces/contracts/solidity-utils/openzeppelin/IERC20.sol";
import "@balancer-labs/v2-interfaces/contracts/pool-utils/IRateProvider.sol";

import "@balancer-labs/v2-solidity-utils/contracts/helpers/ERC20Helpers.sol";
import "@balancer-labs/v2-solidity-utils/contracts/helpers/InputHelpers.sol";
import "@balancer-labs/v2-pool-utils/contracts/rates/PriceRateCache.sol";

import "./ComposableStablePoolStorage.sol";

abstract contract ComposableStablePoolRates is ComposableStablePoolStorage {
    using PriceRateCache for bytes32;
    using FixedPoint for uint256;

    struct RatesParams {
        IERC20[] tokens;
        IRateProvider[] rateProviders;
        uint256[] tokenRateCacheDurations;
    }

    // Token rate caches are used to avoid querying the price rate for a token every time we need to work with it.
    // The "old rate" field is used for precise protocol fee calculation, to ensure that token yield is only
    // "taxed" once. The data structure is as follows:
    //
    // [ expires | duration | old rate | current rate ]
    // [ uint32  |  uint32  |  uint96  |   uint96     ]

    // Since we never need just one cache but all of them at once, instead of making the mapping go from token address
    // to cache, we go from token index (including BPT), i.e. an array. We use a mapping however instead of a native
    // array to skip the extra read associated with the out-of-bounds check, as we have cheaper ways to guarantee the
    // indices are valid.
    mapping(uint256 => bytes32) internal _tokenRateCaches;

    event TokenRateCacheUpdated(uint256 indexed tokenIndex, uint256 rate);
    event TokenRateProviderSet(uint256 indexed tokenIndex, IRateProvider indexed provider, uint256 cacheDuration);

    constructor(RatesParams memory rateParams) {
        InputHelpers.ensureInputLengthMatch(
            rateParams.tokens.length,
            rateParams.rateProviders.length,
            rateParams.tokenRateCacheDurations.length
        );

        IERC20[] memory registeredTokens = _insertSorted(rateParams.tokens, IERC20(this));
        uint256 bptIndex;
        for (
            bptIndex = registeredTokens.length - 1;
            bptIndex > 0 && registeredTokens[bptIndex] > IERC20(this);
            bptIndex--
        ) {
            // solhint-disable-previous-line no-empty-blocks
        }

        uint256 skipBpt = 0;
        for (uint256 i = 0; i < rateParams.tokens.length; i++) {
            if (i == bptIndex) {
                skipBpt = 1;
            }

            uint256 k = i + skipBpt;
            if (rateParams.rateProviders[i] != IRateProvider(0)) {
                _updateTokenRateCache(k, rateParams.rateProviders[i], rateParams.tokenRateCacheDurations[i]);

                emit TokenRateProviderSet(k, rateParams.rateProviders[i], rateParams.tokenRateCacheDurations[i]);

                // Initialize the old rates as well, in case they are referenced before the first join.
                _updateOldRate(k);
            }
        }
    }

    /**
     * @dev Ensure we are not in a Vault context when this function is called, by attempting a no-op internal
     * balance operation. If we are already in a Vault transaction (e.g., a swap, join, or exit), the Vault's
     * reentrancy protection will cause this function to revert.
     *
     * The exact function call doesn't really matter: we're just trying to trigger the Vault reentrancy check
     * (and not hurt anything in case it works). An empty operation array with no specific operation at all works
     * for that purpose, and is also the least expensive in terms of gas and bytecode size.
     *
     * Use this modifier with any function that can cause a state change in a pool and is either public itself,
     * or called by a public function *outside* a Vault operation (e.g., join, exit, or swap).
     * See https://forum.balancer.fi/t/reentrancy-vulnerability-scope-expanded/4345 for reference.
     */
    modifier whenNotInVaultContext() {
        _ensureNotInVaultContext();
        _;
    }

    /**
     * @dev Reverts if called in the middle of a Vault operation; has no effect otherwise.
     */
    function _ensureNotInVaultContext() private {
        IVault.UserBalanceOp[] memory noop = new IVault.UserBalanceOp[](0);
        getVault().manageUserBalance(noop);
    }

    /**
     * @dev Updates the old rate for the token at `index` (including BPT). Assumes `index` is valid.
     */
    function _updateOldRate(uint256 index) internal {
        bytes32 cache = _tokenRateCaches[index];
        _tokenRateCaches[index] = cache.updateOldRate();
    }

    /**
     * @dev Returns the rate for a given token. All token rates are fixed-point values with 18 decimals.
     * If there is no rate provider for the provided token, it returns FixedPoint.ONE.
     */
    function getTokenRate(IERC20 token) external view returns (uint256) {
        return _getTokenRate(_getTokenIndex(token));
    }

    function _getTokenRate(uint256 index) internal view virtual returns (uint256) {
        // We optimize for the scenario where all tokens have rate providers, except the BPT (which never has a rate
        // provider). Therefore, we return early if `token` is the BPT, and otherwise optimistically read the cache
        // expecting that it will not be empty (instead of e.g. fetching the provider to avoid a cache read, since
        // we don't need the provider at all).

        if (index == getBptIndex()) {
            return FixedPoint.ONE;
        }

        bytes32 tokenRateCache = _tokenRateCaches[index];
        return tokenRateCache == bytes32(0) ? FixedPoint.ONE : tokenRateCache.getCurrentRate();
    }

    /**
     * @dev Returns the cached value for token's rate. Reverts if the token doesn't belong to the pool or has no rate
     * provider.
     */
    function getTokenRateCache(IERC20 token)
        external
        view
        returns (
            uint256 rate,
            uint256 oldRate,
            uint256 duration,
            uint256 expires
        )
    {
        bytes32 cache = _tokenRateCaches[_getTokenIndex(token)];

        // A zero cache indicates that the token doesn't have a rate provider associated with it.
        _require(cache != bytes32(0), Errors.TOKEN_DOES_NOT_HAVE_RATE_PROVIDER);

        rate = cache.getCurrentRate();
        oldRate = cache.getOldRate();
        (duration, expires) = cache.getTimestamps();
    }

    /**
     * @dev Sets a new duration for a token rate cache.
     * Note this function also updates the current cached value.
     *
     * This function will revert when called within a Vault context (i.e. in the middle of a join or an exit).
     *
     * This function depends on `getRate` via the rate provider, which may be calculated incorrectly in the middle of a
     * join or an exit because the state of the pool could be out of sync with the state of the Vault.
     *
     * It will also revert if there was no rate provider set initially.
     *
     * See https://forum.balancer.fi/t/reentrancy-vulnerability-scope-expanded/4345 for reference.
     *
     * @param duration Number of seconds until the current token rate is fetched again.
     */
    function setTokenRateCacheDuration(IERC20 token, uint256 duration) external authenticate whenNotInVaultContext {
        uint256 index = _getTokenIndex(token);
        IRateProvider provider = _getRateProvider(index);
        _require(address(provider) != address(0), Errors.TOKEN_DOES_NOT_HAVE_RATE_PROVIDER);
        _updateTokenRateCache(index, provider, duration);
        emit TokenRateProviderSet(index, provider, duration);
    }

    /**
     * @dev Forces a rate cache hit for a token.
     *
     * This function will revert when called within a Vault context (i.e. in the middle of a join or an exit).
     *
     * This function depends on `getRate` via the rate provider, which may be calculated incorrectly in the middle of a
     * join or an exit because the state of the pool could be out of sync with the state of the Vault.
     *
     * It will also revert if the requested token does not have an associated rate provider.
     *
     * See https://forum.balancer.fi/t/reentrancy-vulnerability-scope-expanded/4345 for reference.
     */
    function updateTokenRateCache(IERC20 token) external whenNotInVaultContext {
        uint256 index = _getTokenIndex(token);

        IRateProvider provider = _getRateProvider(index);
        _require(address(provider) != address(0), Errors.TOKEN_DOES_NOT_HAVE_RATE_PROVIDER);
        uint256 duration = _tokenRateCaches[index].getDuration();
        _updateTokenRateCache(index, provider, duration);
    }

    /**
     * @dev Internal function to update a token rate cache for a known provider and duration.
     * It trusts the given values, and does not perform any checks.
     */
    function _updateTokenRateCache(
        uint256 index,
        IRateProvider provider,
        uint256 duration
    ) internal virtual {
        uint256 rate = provider.getRate();
        bytes32 cache = _tokenRateCaches[index];

        _tokenRateCaches[index] = cache.updateRateAndDuration(rate, duration);

        emit TokenRateCacheUpdated(index, rate);
    }

    /**
     * @dev Caches the rates of all tokens if necessary
     */
    function _cacheTokenRatesIfNecessary() internal {
        uint256 totalTokens = _getTotalTokens();
        for (uint256 i = 0; i < totalTokens; ++i) {
            _cacheTokenRateIfNecessary(i);
        }
    }

    /**
     * @dev Caches the rate for a token if necessary. It ignores the call if there is no provider set.
     */
    function _cacheTokenRateIfNecessary(uint256 index) internal {
        // We optimize for the scenario where all tokens have rate providers, except the BPT (which never has a rate
        // provider). Therefore, we return early if token is BPT, and otherwise optimistically read the cache expecting
        // that it will not be empty (instead of e.g. fetching the provider to avoid a cache read in situations where
        // we might not need the provider if the cache is still valid).

        if (index == getBptIndex()) return;

        bytes32 cache = _tokenRateCaches[index];
        if (cache != bytes32(0)) {
            (uint256 duration, uint256 expires) = cache.getTimestamps();
            if (block.timestamp > expires) {
                // solhint-disable-previous-line not-rely-on-time
                _updateTokenRateCache(index, _getRateProvider(index), duration);
            }
        }
    }

    // To compute the yield protocol fees, we need the oldRate for all tokens, even if the exempt flag is not set.
    // We do need to ensure the token has a rate provider before updating; otherwise it will not be in the cache.
    function _updateOldRates() internal {
        uint256 totalTokens = _getTotalTokens();
        for (uint256 i = 0; i < totalTokens; ++i) {
            if (_hasRateProvider(i)) _updateOldRate(i);
        }
    }

    /**
     * @dev Apply the token ratios to a set of balances, only if they have a rate provider.
     * The `balances` array is assumed to not include BPT to ensure that token indices align.
     */
    function _getAdjustedBalances(uint256[] memory balances) internal view returns (uint256[] memory) {
        uint256 totalTokensWithoutBpt = balances.length;
        uint256[] memory adjustedBalances = new uint256[](totalTokensWithoutBpt);

        for (uint256 i = 0; i < totalTokensWithoutBpt; ++i) {
            uint256 skipBptIndex = i >= getBptIndex() ? i + 1 : i;
            adjustedBalances[i] = _hasRateProvider(skipBptIndex)
                ? _adjustedBalance(balances[i], _tokenRateCaches[skipBptIndex])
                : balances[i];
        }

        return adjustedBalances;
    }

    // Compute balance * oldRate/currentRate, doing division last to minimize rounding error.
    function _adjustedBalance(uint256 balance, bytes32 cache) private pure returns (uint256) {
        return Math.divDown(Math.mul(balance, cache.getOldRate()), cache.getCurrentRate());
    }

    // Scaling Factors

    /**
     * @dev Overrides scaling factor getter to compute the tokens' rates.
     */
    function _scalingFactors() internal view virtual override returns (uint256[] memory) {
        // There is no need to check the arrays length since both are based on `_getTotalTokens`
        uint256 totalTokens = _getTotalTokens();
        uint256[] memory scalingFactors = new uint256[](totalTokens);

        for (uint256 i = 0; i < totalTokens; ++i) {
            scalingFactors[i] = _getScalingFactor(i).mulDown(_getTokenRate(i));
        }

        return scalingFactors;
    }

    /**
     * @dev Overrides only owner action to allow setting the cache duration for the token rates
     */
    function _isOwnerOnlyAction(bytes32 actionId) internal view virtual override returns (bool) {
        return (actionId == getActionId(this.setTokenRateCacheDuration.selector)) || super._isOwnerOnlyAction(actionId);
    }
}

// File: contracts/ComposableStablePoolProtocolFees.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 "@balancer-labs/v2-solidity-utils/contracts/math/FixedPoint.sol";
import "@balancer-labs/v2-solidity-utils/contracts/helpers/WordCodec.sol";
import "@balancer-labs/v2-pool-utils/contracts/protocol-fees/ProtocolFeeCache.sol";
import "@balancer-labs/v2-pool-utils/contracts/protocol-fees/InvariantGrowthProtocolSwapFees.sol";

import "./ComposableStablePoolStorage.sol";
import "./ComposableStablePoolRates.sol";
import "./StableMath.sol";

abstract contract ComposableStablePoolProtocolFees is
    ComposableStablePoolStorage,
    ComposableStablePoolRates,
    ProtocolFeeCache
{
    using FixedPoint for uint256;
    using WordCodec for bytes32;

    // To track protocol fees, we measure and store the value of the invariant after every join and exit.
    // All invariant growth that happens between join and exit events is due to swap fees and yield.
    // For selected tokens, we exclude the yield portion from the computation.
    // Because the invariant depends on the amplification parameter, and this value may change over time, we should only
    // compare invariants that were computed using the same value. We therefore store both values together.
    //
    // These values reside in the same storage slot. The amplification factor is bound by _MAX_AMP * _AMP_PRECISION, or
    // 5e6, which fits in 23 bits. We use all remaining bits for the invariant: this is more than enough, as the
    // invariant is proportional to the total supply, which is capped at 112 bits.
    // The data structure is as follows:
    //
    // [ last join-exit amplification  | last post join-exit invariant ]
    // [           23 bits             |            233 bits           ]
    bytes32 private _lastJoinExitData;

    uint256 private constant _LAST_POST_JOIN_EXIT_INVARIANT_OFFSET = 0;
    uint256 private constant _LAST_POST_JOIN_EXIT_INVARIANT_SIZE = 233;
    uint256 private constant _LAST_JOIN_EXIT_AMPLIFICATION_OFFSET = _LAST_POST_JOIN_EXIT_INVARIANT_OFFSET +
        _LAST_POST_JOIN_EXIT_INVARIANT_SIZE;

    uint256 private constant _LAST_JOIN_EXIT_AMPLIFICATION_SIZE = 23;

    /**
     * @dev Calculates due protocol fees originating from accumulated swap fees and yield of non-exempt tokens, pays
     * them by minting BPT, and returns the actual supply and current balances.
     *
     * We also return the current invariant computed using the amplification factor at the last join or exit, which can
     * be useful to skip computations in scenarios where the amplification factor is not changing.
     */
    function _payProtocolFeesBeforeJoinExit(
        uint256[] memory registeredBalances,
        uint256 lastJoinExitAmp,
        uint256 lastPostJoinExitInvariant
    )
        internal
        returns (
            uint256,
            uint256[] memory,
            uint256
        )
    {
        (uint256 virtualSupply, uint256[] memory balances) = _dropBptItemFromBalances(registeredBalances);

        // First, we'll compute what percentage of the Pool the protocol should own due to charging protocol fees on
        // swap fees and yield.
        (
            uint256 expectedProtocolOwnershipPercentage,
            uint256 currentInvariantWithLastJoinExitAmp
        ) = _getProtocolPoolOwnershipPercentage(balances, lastJoinExitAmp, lastPostJoinExitInvariant);

        // Now that we know what percentage of the Pool's current value the protocol should own, we can compute how
        // much BPT we need to mint to get to this state. Since we're going to mint BPT for the protocol, the value
        // of each BPT is going to be reduced as all LPs get diluted.
        uint256 protocolFeeAmount = ProtocolFees.bptForPoolOwnershipPercentage(
            virtualSupply,
            expectedProtocolOwnershipPercentage
        );

        if (protocolFeeAmount > 0) {
            _payProtocolFees(protocolFeeAmount);
        }

        // We pay fees before a join or exit to ensure the pool is debt-free. This increases the virtual supply (making
        // it match the actual supply).
        //
        // For this addition to overflow, `totalSupply` would also have already overflowed.
        return (virtualSupply + protocolFeeAmount, balances, currentInvariantWithLastJoinExitAmp);
    }

    function _getProtocolPoolOwnershipPercentage(
        uint256[] memory balances,
        uint256 lastJoinExitAmp,
        uint256 lastPostJoinExitInvariant
    ) internal view returns (uint256, uint256) {
        // We compute three invariants, adjusting the balances of tokens that have rate providers by undoing the current
        // rate adjustment and then applying the old rate. This is equivalent to multiplying by old rate / current rate.
        //
        // In all cases we compute invariants with the last join-exit amplification factor, so that changes to the
        // amplification are not translated into changes to the invariant. Since amplification factor changes are both
        // infrequent and slow, they should have little effect on the pool balances, making this a very good
        // approximation.
        //
        // With this technique we obtain an invariant that does not include yield at all, meaning any growth will be due
        // exclusively to swap fees. We call this the 'swap fee growth invariant'.
        // A second invariant will exclude the yield of exempt tokens, and therefore include both swap fees and
        // non-exempt yield. This is called the 'non exempt growth invariant'.
        // Finally, a third invariant includes the yield of all tokens by using only the current rates. We call this the
        // 'total growth invariant', since it includes both swap fee growth, non-exempt yield growth and exempt yield
        // growth. If the last join-exit amplification equals the current one, this invariant equals the current
        // invariant.

        (
            uint256 swapFeeGrowthInvariant,
            uint256 totalNonExemptGrowthInvariant,
            uint256 totalGrowthInvariant
        ) = _getGrowthInvariants(balances, lastJoinExitAmp, lastPostJoinExitInvariant);

        // By comparing the invariant increase attributable to each source of growth to the total growth invariant,
        // we can calculate how much of the current Pool value originates from that source, and then apply the
        // corresponding protocol fee percentage to that amount.

        // We have two sources of growth: swap fees, and non-exempt yield. As we illustrate graphically below:
        //
        // growth due to swap fees        = (swap fee growth invariant - last post join-exit invariant)
        // growth due to non-exempt yield = (non-exempt growth invariant - swap fee growth invariant)
        //
        // These can be converted to additive percentages by normalizing against the total growth invariant value:
        // growth due to swap fees / total growth invariant = % pool ownership due from swap fees
        // growth due to non-exempt yield / total growth invariant = % pool ownership due from non-exempt yield
        //
        //   ┌───────────────────────┐ ──┐
        //   │  exempt yield         │   │  total growth invariant
        //   ├───────────────────────┤   │ ──┐
        //   │  non-exempt yield     │   │   │  non-exempt growth invariant
        //   ├───────────────────────┤   │   │ ──┐
        //   │  swap fees            │   │   │   │  swap fee growth invariant
        //   ├───────────────────────┤   │   │   │ ──┐
        //   │   original value      │   │   │   │   │  last post join-exit invariant
        //   └───────────────────────┘ ──┘ ──┘ ──┘ ──┘
        //
        // Each invariant should be larger than its precedessor. In case any rounding error results in them being
        // smaller, we adjust the subtraction to equal 0.

        // Note: in the unexpected scenario where the rates of the tokens shrink over time instead of growing (i.e. if
        // the yield is negative), the non-exempt growth invariant might actually be *smaller* than the swap fee growth
        // invariant, and the total growth invariant might be *smaller* than the non-exempt growth invariant. Depending
        // on the order in which swaps, joins/exits and rate changes happen, as well as their relative magnitudes, it is
        // possible for the Pool to either pay more or less protocol fees than it should.

        // This patched version handles these edge cases gracefully, as it 1) forcibly bounds the swap fee growth
        // invariant between the total growth and last post join-exit invariant; 2) enforces "all or nothing" exempt
        // flags, which constrains the non-exempt growth invariant to be equal to either the total growth or swap
        // fee growth invariant.
        //
        // Furthermore, the protocol ownership percentage is hard-coded to zero (so protocol fees will be zero),
        // if the total growth invariant has gone *down* since the last join or exit, which is possible if rates
        // declined. Together, these measures ensure protocol fee amounts will be bound by the non-manipulable
        // swap fee growth, or zero in any pathological situations.

        // If the total invariant decreased or stayed the same, there is no growth to split between swap and yield fees.
        if (totalGrowthInvariant <= lastPostJoinExitInvariant) {
            return (0, totalGrowthInvariant);
        }

        // By now, the following inequality applies:
        // totalGrowthInvariant >= totalNonExemptGrowthInvariant >= swapFeeGrowthInvariant >= lastPostJoinExitInvariant
        // So these differences are safe to execute; their lower bound is 0 and they will not overflow.
        uint256 swapFeeGrowthInvariantDelta = swapFeeGrowthInvariant - lastPostJoinExitInvariant;
        uint256 nonExemptYieldGrowthInvariantDelta = totalNonExemptGrowthInvariant - swapFeeGrowthInvariant;

        // We can now derive what percentage of the Pool's total value each invariant delta represents by dividing by
        // the total growth invariant. These values, multiplied by the protocol fee percentage for each growth type,
        // represent the percentage of Pool ownership the protocol should have due to each source.

        uint256 protocolSwapFeePercentage = swapFeeGrowthInvariantDelta.divDown(totalGrowthInvariant).mulDown(
            getProtocolFeePercentageCache(ProtocolFeeType.SWAP)
        );

        uint256 protocolYieldPercentage = nonExemptYieldGrowthInvariantDelta.divDown(totalGrowthInvariant).mulDown(
            getProtocolFeePercentageCache(ProtocolFeeType.YIELD)
        );

        // These percentages can then be simply added to compute the total protocol Pool ownership percentage.
        // This is naturally bounded above by FixedPoint.ONE so this addition cannot overflow.
        return (protocolSwapFeePercentage + protocolYieldPercentage, totalGrowthInvariant);
    }

    /**
     * @dev Returns total growth invariant and swap / yield invariant approximations.
     * The calculated invariants are bounded such that:
     *
     * - if totalGrowthInvariant <= lastPostJoinExitInvariant, the total value has decreased, so we can skip all
     * other invariant calculations and just return `totalGrowthInvariant` for all. Protocol fees should be zero
     * in this case, so callers using this to compute fees must also check for this, and return zero for the
     * protocol ownership percentage.
     *
     * - Otherwise, totalGrowthInvariant >= totalNonExemptGrowthInvariant >=
     *     swapFeeGrowthInvariant >= lastPostJoinExitInvariant
     * This was previously an assumption, but is now ensured by the logic in this function.
     */
    function _getGrowthInvariants(
        uint256[] memory balances,
        uint256 lastJoinExitAmp,
        uint256 lastPostJoinExitInvariant
    )
        internal
        view
        returns (
            uint256 swapFeeGrowthInvariant,
            uint256 totalNonExemptGrowthInvariant,
            uint256 totalGrowthInvariant
        )
    {
        // Total growth invariant is always calculated with the current (scaled / unadjusted) balances.
        totalGrowthInvariant = StableMath._calculateInvariant(lastJoinExitAmp, balances);

        // If total invariant decreased, calculating the other approximations is unnecessary.
        if (totalGrowthInvariant <= lastPostJoinExitInvariant) {
            return (totalGrowthInvariant, totalGrowthInvariant, totalGrowthInvariant);
        }

        // Swap fee invariant is calculated with adjusted balances, to discount the yield.
        swapFeeGrowthInvariant = StableMath._calculateInvariant(
            lastJoinExitAmp,
            _getAdjustedBalances(balances) // Adjust all token balances with rate providers.
        );

        // The `swapFeeGrowthInvariant` cannot ever be outside the bounds:
        // totalGrowthInvariant >= swapFeeGrowthInvariant >= lastPostJoinExitInvariant
        swapFeeGrowthInvariant = Math.min(totalGrowthInvariant, swapFeeGrowthInvariant); // Set upper bound.
        swapFeeGrowthInvariant = Math.max(lastPostJoinExitInvariant, swapFeeGrowthInvariant); // Set lower bound.

        // The only two accepted possibilities are either all tokens exempt, or none tokens exempt.
        // totalNonExemptGrowthInvariant will either be totalGrowthInvariant or swapFeeGrowthInvariant.
        // At this point,
        // - totalGrowthInvariant > lastPostJoinExitInvariant
        // - totalGrowthInvariant >= swapFeeGrowthInvariant >= lastPostJoinExitInvariant
        // So the complete inequality will apply by the end of this function:
        // totalGrowthInvariant >= totalNonExemptGrowthInvariant >= swapFeeGrowthInvariant >= lastPostJoinExitInvariant
        if (isExemptFromYieldProtocolFee()) {
            // If no tokens are charged fees on yield, then the non-exempt growth is equal to the swap fee growth - no
            // yield fees will be collected.

            totalNonExemptGrowthInvariant = swapFeeGrowthInvariant;
        } else {
            // If there are no tokens with fee-exempt yield, then the total non-exempt growth will equal the total
            // growth: all yield growth is non-exempt. There's also no point in adjusting balances, since we
            // already know none are exempt.

            totalNonExemptGrowthInvariant = totalGrowthInvariant;
        }
    }

    /**
     * @dev Store the latest invariant based on the adjusted balances after the join or exit, using current rates.
     * Also cache the amp factor, so that the invariant is not affected by amp updates between joins and exits.
     *
     * Pay protocol fees due on any current join or exit swap.
     */
    function _updateInvariantAfterJoinExit(
        uint256 currentAmp,
        uint256[] memory balances,
        uint256 preJoinExitInvariant,
        uint256 preJoinExitSupply,
        uint256 postJoinExitSupply
    ) internal {
        // `_payProtocolFeesBeforeJoinExit` paid protocol fees accumulated between the previous and current
        // join or exit, while this code pays any protocol fees due on the current join or exit.
        // The amp and rates are constant during a single transaction, so it doesn't matter if there
        // is an ongoing amp change, and we can ignore yield.

        // Compute the growth ratio between the pre- and post-join/exit balances.
        // Note that the pre-join/exit invariant is *not* the invariant from the last join,
        // but computed from the balances before this particular join/exit.

        uint256 postJoinExitInvariant = StableMath._calculateInvariant(currentAmp, balances);

        // Compute the portion of the invariant increase due to fees
        uint256 supplyGrowthRatio = postJoinExitSupply.divDown(preJoinExitSupply);
        uint256 feelessInvariant = preJoinExitInvariant.mulDown(supplyGrowthRatio);

        // The postJoinExitInvariant should always be greater than the feelessInvariant (since the invariant and total
        // supply move proportionally outside of fees, which the postJoinInvariant includes and the feelessInvariant
        // does not). However, in the unexpected case in which due to rounding errors this is not true, we simply skip
        // further computation of protocol fees.
        if (postJoinExitInvariant > feelessInvariant) {
            uint256 invariantDeltaFromFees = postJoinExitInvariant - feelessInvariant;

            // To convert to a percentage of pool ownership, multiply by the rate,
            // then normalize against the final invariant
            uint256 protocolOwnershipPercentage = Math.divDown(
                Math.mul(invariantDeltaFromFees, getProtocolFeePercentageCache(ProtocolFeeType.SWAP)),
                postJoinExitInvariant
            );

            if (protocolOwnershipPercentage > 0) {
                uint256 protocolFeeAmount = ProtocolFees.bptForPoolOwnershipPercentage(
                    postJoinExitSupply,
                    protocolOwnershipPercentage
                );

                _payProtocolFees(protocolFeeAmount);
            }
        }

        _updatePostJoinExit(currentAmp, postJoinExitInvariant);
    }

    /**
     * @dev Update the stored values of the amp and final post-join/exit invariant, to reset the basis for protocol
     * swap fees. Also copy the current rates to the old rates, to establish the new protocol yield basis for protocol
     * yield fees.
     */
    function _updatePostJoinExit(uint256 currentAmp, uint256 postJoinExitInvariant) internal {
        _lastJoinExitData =
            WordCodec.encodeUint(currentAmp, _LAST_JOIN_EXIT_AMPLIFICATION_OFFSET, _LAST_JOIN_EXIT_AMPLIFICATION_SIZE) |
            WordCodec.encodeUint(
                postJoinExitInvariant,
                _LAST_POST_JOIN_EXIT_INVARIANT_OFFSET,
                _LAST_POST_JOIN_EXIT_INVARIANT_SIZE
            );

        _updateOldRates();
    }

    /**
     * @notice Return the amplification factor and invariant as of the most recent join or exit (including BPT swaps)
     */
    function getLastJoinExitData()
        public
        view
        returns (uint256 lastJoinExitAmplification, uint256 lastPostJoinExitInvariant)
    {
        bytes32 rawData = _lastJoinExitData;

        lastJoinExitAmplification = rawData.decodeUint(
            _LAST_JOIN_EXIT_AMPLIFICATION_OFFSET,
            _LAST_JOIN_EXIT_AMPLIFICATION_SIZE
        );

        lastPostJoinExitInvariant = rawData.decodeUint(
            _LAST_POST_JOIN_EXIT_INVARIANT_OFFSET,
            _LAST_POST_JOIN_EXIT_INVARIANT_SIZE
        );
    }

    /**
     * @dev Inheritance rules still require us to override this in the most derived contract, even though
     * it only calls super.
     */
    function _isOwnerOnlyAction(bytes32 actionId)
        internal
        view
        virtual
        override(
            // Our inheritance pattern creates a small diamond that requires explicitly listing the parents here.
            // Each parent calls the `super` version, so linearization ensures all implementations are called.
            BasePool,
            BasePoolAuthorization,
            ComposableStablePoolRates
        )
        returns (bool)
    {
        return super._isOwnerOnlyAction(actionId);
    }
}

// File: contracts/StablePoolAmplification.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 "@balancer-labs/v2-pool-utils/contracts/BasePoolAuthorization.sol";
import "@balancer-labs/v2-solidity-utils/contracts/helpers/WordCodec.sol";

import "./StableMath.sol";

abstract contract StablePoolAmplification is BasePoolAuthorization {
    using WordCodec for bytes32;

    // This contract uses timestamps to slowly update its Amplification parameter over time. These changes must occur
    // over a minimum time period much larger than the blocktime, making timestamp manipulation a non-issue.
    // solhint-disable not-rely-on-time

    // Amplification factor changes must happen over a minimum period of one day, and can at most divide or multiply the
    // current value by 2 every day.
    // WARNING: this only limits *a single* amplification change to have a maximum rate of change of twice the original
    // value daily. It is possible to perform multiple amplification changes in sequence to increase this value more
    // rapidly: for example, by doubling the value every day it can increase by a factor of 8 over three days (2^3).
    uint256 private constant _MIN_UPDATE_TIME = 1 days;
    uint256 private constant _MAX_AMP_UPDATE_DAILY_RATE = 2;

    // The amplification data structure is as follows:
    // [  64 bits |   64 bits  |  64 bits  |   64 bits   ]
    // [ end time | start time | end value | start value ]
    // |MSB                                           LSB|

    uint256 private constant _AMP_START_VALUE_OFFSET = 0;
    uint256 private constant _AMP_END_VALUE_OFFSET = 64;
    uint256 private constant _AMP_START_TIME_OFFSET = 128;
    uint256 private constant _AMP_END_TIME_OFFSET = 192;

    uint256 private constant _AMP_VALUE_BIT_LENGTH = 64;
    uint256 private constant _AMP_TIMESTAMP_BIT_LENGTH = 64;

    bytes32 private _packedAmplificationData;

    event AmpUpdateStarted(uint256 startValue, uint256 endValue, uint256 startTime, uint256 endTime);
    event AmpUpdateStopped(uint256 currentValue);

    constructor(uint256 amplificationParameter) {
        _require(amplificationParameter >= StableMath._MIN_AMP, Errors.MIN_AMP);
        _require(amplificationParameter <= StableMath._MAX_AMP, Errors.MAX_AMP);

        uint256 initialAmp = Math.mul(amplificationParameter, StableMath._AMP_PRECISION);
        _setAmplificationData(initialAmp);
    }

    function getAmplificationParameter()
        external
        view
        returns (
            uint256 value,
            bool isUpdating,
            uint256 precision
        )
    {
        (value, isUpdating) = _getAmplificationParameter();
        precision = StableMath._AMP_PRECISION;
    }

    // Return the current amp value, which will be an interpolation if there is an ongoing amp update.
    // Also return a flag indicating whether there is an ongoing update.
    function _getAmplificationParameter() internal view returns (uint256 value, bool isUpdating) {
        (uint256 startValue, uint256 endValue, uint256 startTime, uint256 endTime) = _getAmplificationData();

        // Note that block.timestamp >= startTime, since startTime is set to the current time when an update starts

        if (block.timestamp < endTime) {
            isUpdating = true;

            // We can skip checked arithmetic as:
            //  - block.timestamp is always larger or equal to startTime
            //  - endTime is always larger than startTime
            //  - the value delta is bounded by the largest amplification parameter, which never causes the
            //    multiplication to overflow.
            // This also means that the following computation will never revert nor yield invalid results.
            if (endValue > startValue) {
                value = startValue + ((endValue - startValue) * (block.timestamp - startTime)) / (endTime - startTime);
            } else {
                value = startValue - ((startValue - endValue) * (block.timestamp - startTime)) / (endTime - startTime);
            }
        } else {
            isUpdating = false;
            value = endValue;
        }
    }

    // Unpack and return all amplification-related parameters.
    function _getAmplificationData()
        private
        view
        returns (
            uint256 startValue,
            uint256 endValue,
            uint256 startTime,
            uint256 endTime
        )
    {
        startValue = _packedAmplificationData.decodeUint(_AMP_START_VALUE_OFFSET, _AMP_VALUE_BIT_LENGTH);
        endValue = _packedAmplificationData.decodeUint(_AMP_END_VALUE_OFFSET, _AMP_VALUE_BIT_LENGTH);
        startTime = _packedAmplificationData.decodeUint(_AMP_START_TIME_OFFSET, _AMP_TIMESTAMP_BIT_LENGTH);
        endTime = _packedAmplificationData.decodeUint(_AMP_END_TIME_OFFSET, _AMP_TIMESTAMP_BIT_LENGTH);
    }

    /**
     * @dev Begin changing the amplification parameter to `rawEndValue` over time. The value will change linearly until
     * `endTime` is reached, when it will be `rawEndValue`.
     *
     * NOTE: Internally, the amplification parameter is represented using higher precision. The values returned by
     * `getAmplificationParameter` have to be corrected to account for this when comparing to `rawEndValue`.
     */
    function startAmplificationParameterUpdate(uint256 rawEndValue, uint256 endTime) external authenticate {
        _require(rawEndValue >= StableMath._MIN_AMP, Errors.MIN_AMP);
        _require(rawEndValue <= StableMath._MAX_AMP, Errors.MAX_AMP);

        uint256 duration = Math.sub(endTime, block.timestamp);
        _require(duration >= _MIN_UPDATE_TIME, Errors.AMP_END_TIME_TOO_CLOSE);

        (uint256 currentValue, bool isUpdating) = _getAmplificationParameter();
        _require(!isUpdating, Errors.AMP_ONGOING_UPDATE);

        uint256 endValue = Math.mul(rawEndValue, StableMath._AMP_PRECISION);

        // daily rate = (endValue / currentValue) / duration * 1 day
        // We perform all multiplications first to not reduce precision, and round the division up as we want to avoid
        // large rates. Note that these are regular integer multiplications and divisions, not fixed point.
        uint256 dailyRate = endValue > currentValue
            ? Math.divUp(Math.mul(1 days, endValue), Math.mul(currentValue, duration))
            : Math.divUp(Math.mul(1 days, currentValue), Math.mul(endValue, duration));
        _require(dailyRate <= _MAX_AMP_UPDATE_DAILY_RATE, Errors.AMP_RATE_TOO_HIGH);

        _setAmplificationData(currentValue, endValue, block.timestamp, endTime);
    }

    /**
     * @dev Stops the amplification parameter change process, keeping the current value.
     */
    function stopAmplificationParameterUpdate() external authenticate {
        (uint256 currentValue, bool isUpdating) = _getAmplificationParameter();
        _require(isUpdating, Errors.AMP_NO_ONGOING_UPDATE);

        _setAmplificationData(currentValue);
    }

    function _setAmplificationData(uint256 value) private {
        _storeAmplificationData(value, value, block.timestamp, block.timestamp);
        emit AmpUpdateStopped(value);
    }

    function _setAmplificationData(
        uint256 startValue,
        uint256 endValue,
        uint256 startTime,
        uint256 endTime
    ) private {
        _storeAmplificationData(startValue, endValue, startTime, endTime);
        emit AmpUpdateStarted(startValue, endValue, startTime, endTime);
    }

    function _storeAmplificationData(
        uint256 startValue,
        uint256 endValue,
        uint256 startTime,
        uint256 endTime
    ) private {
        _packedAmplificationData =
            WordCodec.encodeUint(startValue, _AMP_START_VALUE_OFFSET, _AMP_VALUE_BIT_LENGTH) |
            WordCodec.encodeUint(endValue, _AMP_END_VALUE_OFFSET, _AMP_VALUE_BIT_LENGTH) |
            WordCodec.encodeUint(startTime, _AMP_START_TIME_OFFSET, _AMP_TIMESTAMP_BIT_LENGTH) |
            WordCodec.encodeUint(endTime, _AMP_END_TIME_OFFSET, _AMP_TIMESTAMP_BIT_LENGTH);
    }

    // Permissioned functions

    /**
     * @dev Overrides only owner action to allow setting the cache duration for the token rates
     */
    function _isOwnerOnlyAction(bytes32 actionId) internal view virtual override returns (bool) {
        return
            (actionId == getActionId(this.startAmplificationParameterUpdate.selector)) ||
            (actionId == getActionId(this.stopAmplificationParameterUpdate.selector)) ||
            super._isOwnerOnlyAction(actionId);
    }
}

// File: contracts/StableMath.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 "@balancer-labs/v2-solidity-utils/contracts/math/FixedPoint.sol";
import "@balancer-labs/v2-solidity-utils/contracts/math/Math.sol";

// These functions start with an underscore, as if they were part of a contract and not a library. At some point this
// should be fixed. Additionally, some variables have non mixed case names (e.g. P_D) that relate to the mathematical
// derivations.
// solhint-disable private-vars-leading-underscore, var-name-mixedcase

library StableMath {
    using FixedPoint for uint256;

    uint256 internal constant _MIN_AMP = 1;
    uint256 internal constant _MAX_AMP = 5000;
    uint256 internal constant _AMP_PRECISION = 1e3;

    uint256 internal constant _MAX_STABLE_TOKENS = 5;

    // Note on unchecked arithmetic:
    // This contract performs a large number of additions, subtractions, multiplications and divisions, often inside
    // loops. Since many of these operations are gas-sensitive (as they happen e.g. during a swap), it is important to
    // not make any unnecessary checks. We rely on a set of invariants to avoid having to use checked arithmetic (the
    // Math library), including:
    //  - the number of tokens is bounded by _MAX_STABLE_TOKENS
    //  - the amplification parameter is bounded by _MAX_AMP * _AMP_PRECISION, which fits in 23 bits
    //  - the token balances are bounded by 2^112 (guaranteed by the Vault) times 1e18 (the maximum scaling factor),
    //    which fits in 172 bits
    //
    // This means e.g. we can safely multiply a balance by the amplification parameter without worrying about overflow.

    // About swap fees on joins and exits:
    // Any join or exit that is not perfectly balanced (e.g. all single token joins or exits) is mathematically
    // equivalent to a perfectly balanced join or  exit followed by a series of swaps. Since these swaps would charge
    // swap fees, it follows that (some) joins and exits should as well.
    // On these operations, we split the token amounts in 'taxable' and 'non-taxable' portions, where the 'taxable' part
    // is the one to which swap fees are applied.

    // Computes the invariant given the current balances, using the Newton-Raphson approximation.
    // The amplification parameter equals: A n^(n-1)
    // See: https://github.com/curvefi/curve-contract/blob/b0bbf77f8f93c9c5f4e415bce9cd71f0cdee960e/contracts/pool-templates/base/SwapTemplateBase.vy#L206
    // solhint-disable-previous-line max-line-length
    function _calculateInvariant(uint256 amplificationParameter, uint256[] memory balances)
        internal
        pure
        returns (uint256)
    {
        /**********************************************************************************************
        // invariant                                                                                 //
        // D = invariant                                                  D^(n+1)                    //
        // A = amplification coefficient      A  n^n S + D = A D n^n + -----------                   //
        // S = sum of balances                                             n^n P                     //
        // P = product of balances                                                                   //
        // n = number of tokens                                                                      //
        **********************************************************************************************/

        // Always round down, to match Vyper's arithmetic (which always truncates).

        uint256 sum = 0; // S in the Curve version
        uint256 numTokens = balances.length;
        for (uint256 i = 0; i < numTokens; i++) {
            sum = sum.add(balances[i]);
        }
        if (sum == 0) {
            return 0;
        }

        uint256 prevInvariant; // Dprev in the Curve version
        uint256 invariant = sum; // D in the Curve version
        uint256 ampTimesTotal = amplificationParameter * numTokens; // Ann in the Curve version

        for (uint256 i = 0; i < 255; i++) {
            uint256 D_P = invariant;

            for (uint256 j = 0; j < numTokens; j++) {
                // (D_P * invariant) / (balances[j] * numTokens)
                D_P = Math.divDown(Math.mul(D_P, invariant), Math.mul(balances[j], numTokens));
            }

            prevInvariant = invariant;

            invariant = Math.divDown(
                Math.mul(
                    // (ampTimesTotal * sum) / AMP_PRECISION + D_P * numTokens
                    (Math.divDown(Math.mul(ampTimesTotal, sum), _AMP_PRECISION).add(Math.mul(D_P, numTokens))),
                    invariant
                ),
                // ((ampTimesTotal - _AMP_PRECISION) * invariant) / _AMP_PRECISION + (numTokens + 1) * D_P
                (
                    Math.divDown(Math.mul((ampTimesTotal - _AMP_PRECISION), invariant), _AMP_PRECISION).add(
                        Math.mul((numTokens + 1), D_P)
                    )
                )
            );

            if (invariant > prevInvariant) {
                if (invariant - prevInvariant <= 1) {
                    return invariant;
                }
            } else if (prevInvariant - invariant <= 1) {
                return invariant;
            }
        }

        _revert(Errors.STABLE_INVARIANT_DIDNT_CONVERGE);
    }

    // Computes how many tokens can be taken out of a pool if `tokenAmountIn` are sent, given the current balances.
    // The amplification parameter equals: A n^(n-1)
    function _calcOutGivenIn(
        uint256 amplificationParameter,
        uint256[] memory balances,
        uint256 tokenIndexIn,
        uint256 tokenIndexOut,
        uint256 tokenAmountIn,
        uint256 invariant
    ) internal pure returns (uint256) {
        /**************************************************************************************************************
        // outGivenIn token x for y - polynomial equation to solve                                                   //
        // ay = amount out to calculate                                                                              //
        // by = balance token out                                                                                    //
        // y = by - ay (finalBalanceOut)                                                                             //
        // D = invariant                                               D                     D^(n+1)                 //
        // A = amplification coefficient               y^2 + ( S - ----------  - D) * y -  ------------- = 0         //
        // n = number of tokens                                    (A * n^n)               A * n^2n * P              //
        // S = sum of final balances but y                                                                           //
        // P = product of final balances but y                                                                       //
        **************************************************************************************************************/

        // Amount out, so we round down overall.
        balances[tokenIndexIn] = balances[tokenIndexIn].add(tokenAmountIn);

        uint256 finalBalanceOut = _getTokenBalanceGivenInvariantAndAllOtherBalances(
            amplificationParameter,
            balances,
            invariant,
            tokenIndexOut
        );

        // No need to use checked arithmetic since `tokenAmountIn` was actually added to the same balance right before
        // calling `_getTokenBalanceGivenInvariantAndAllOtherBalances` which doesn't alter the balances array.
        balances[tokenIndexIn] = balances[tokenIndexIn] - tokenAmountIn;

        return balances[tokenIndexOut].sub(finalBalanceOut).sub(1);
    }

    // Computes how many tokens must be sent to a pool if `tokenAmountOut` are sent given the
    // current balances, using the Newton-Raphson approximation.
    // The amplification parameter equals: A n^(n-1)
    function _calcInGivenOut(
        uint256 amplificationParameter,
        uint256[] memory balances,
        uint256 tokenIndexIn,
        uint256 tokenIndexOut,
        uint256 tokenAmountOut,
        uint256 invariant
    ) internal pure returns (uint256) {
        /**************************************************************************************************************
        // inGivenOut token x for y - polynomial equation to solve                                                   //
        // ax = amount in to calculate                                                                               //
        // bx = balance token in                                                                                     //
        // x = bx + ax (finalBalanceIn)                                                                              //
        // D = invariant                                                D                     D^(n+1)                //
        // A = amplification coefficient               x^2 + ( S - ----------  - D) * x -  ------------- = 0         //
        // n = number of tokens                                     (A * n^n)               A * n^2n * P             //
        // S = sum of final balances but x                                                                           //
        // P = product of final balances but x                                                                       //
        **************************************************************************************************************/

        // Amount in, so we round up overall.
        balances[tokenIndexOut] = balances[tokenIndexOut].sub(tokenAmountOut);

        uint256 finalBalanceIn = _getTokenBalanceGivenInvariantAndAllOtherBalances(
            amplificationParameter,
            balances,
            invariant,
            tokenIndexIn
        );

        // No need to use checked arithmetic since `tokenAmountOut` was actually subtracted from the same balance right
        // before calling `_getTokenBalanceGivenInvariantAndAllOtherBalances` which doesn't alter the balances array.
        balances[tokenIndexOut] = balances[tokenIndexOut] + tokenAmountOut;

        return finalBalanceIn.sub(balances[tokenIndexIn]).add(1);
    }

    function _calcBptOutGivenExactTokensIn(
        uint256 amp,
        uint256[] memory balances,
        uint256[] memory amountsIn,
        uint256 bptTotalSupply,
        uint256 currentInvariant,
        uint256 swapFeePercentage
    ) internal pure returns (uint256) {
        // BPT out, so we round down overall.

        // First loop calculates the sum of all token balances, which will be used to calculate
        // the current weights of each token, relative to this sum
        uint256 sumBalances = 0;
        for (uint256 i = 0; i < balances.length; i++) {
            sumBalances = sumBalances.add(balances[i]);
        }

        // Calculate the weighted balance ratio without considering fees
        uint256[] memory balanceRatiosWithFee = new uint256[](amountsIn.length);
        // The weighted sum of token balance ratios with fee
        uint256 invariantRatioWithFees = 0;
        for (uint256 i = 0; i < balances.length; i++) {
            uint256 currentWeight = balances[i].divDown(sumBalances);
            balanceRatiosWithFee[i] = balances[i].add(amountsIn[i]).divDown(balances[i]);
            invariantRatioWithFees = invariantRatioWithFees.add(balanceRatiosWithFee[i].mulDown(currentWeight));
        }

        // Second loop calculates new amounts in, taking into account the fee on the percentage excess
        uint256[] memory newBalances = new uint256[](balances.length);
        for (uint256 i = 0; i < balances.length; i++) {
            uint256 amountInWithoutFee;

            // Check if the balance ratio is greater than the ideal ratio to charge fees or not
            if (balanceRatiosWithFee[i] > invariantRatioWithFees) {
                uint256 nonTaxableAmount = balances[i].mulDown(invariantRatioWithFees.sub(FixedPoint.ONE));
                uint256 taxableAmount = amountsIn[i].sub(nonTaxableAmount);
                // No need to use checked arithmetic for the swap fee, it is guaranteed to be lower than 50%
                amountInWithoutFee = nonTaxableAmount.add(taxableAmount.mulDown(FixedPoint.ONE - swapFeePercentage));
            } else {
                amountInWithoutFee = amountsIn[i];
            }

            newBalances[i] = balances[i].add(amountInWithoutFee);
        }

        uint256 newInvariant = _calculateInvariant(amp, newBalances);
        uint256 invariantRatio = newInvariant.divDown(currentInvariant);

        // If the invariant didn't increase for any reason, we simply don't mint BPT
        if (invariantRatio > FixedPoint.ONE) {
            return bptTotalSupply.mulDown(invariantRatio - FixedPoint.ONE);
        } else {
            return 0;
        }
    }

    function _calcTokenInGivenExactBptOut(
        uint256 amp,
        uint256[] memory balances,
        uint256 tokenIndex,
        uint256 bptAmountOut,
        uint256 bptTotalSupply,
        uint256 currentInvariant,
        uint256 swapFeePercentage
    ) internal pure returns (uint256) {
        // Token in, so we round up overall.

        uint256 newInvariant = bptTotalSupply.add(bptAmountOut).divUp(bptTotalSupply).mulUp(currentInvariant);

        // Calculate amount in without fee.
        uint256 newBalanceTokenIndex = _getTokenBalanceGivenInvariantAndAllOtherBalances(
            amp,
            balances,
            newInvariant,
            tokenIndex
        );
        uint256 amountInWithoutFee = newBalanceTokenIndex.sub(balances[tokenIndex]);

        // First calculate the sum of all token balances, which will be used to calculate
        // the current weight of each token
        uint256 sumBalances = 0;
        for (uint256 i = 0; i < balances.length; i++) {
            sumBalances = sumBalances.add(balances[i]);
        }

        // We can now compute how much extra balance is being deposited and used in virtual swaps, and charge swap fees
        // accordingly.
        uint256 currentWeight = balances[tokenIndex].divDown(sumBalances);
        uint256 taxablePercentage = currentWeight.complement();
        uint256 taxableAmount = amountInWithoutFee.mulUp(taxablePercentage);
        uint256 nonTaxableAmount = amountInWithoutFee.sub(taxableAmount);

        // No need to use checked arithmetic for the swap fee, it is guaranteed to be lower than 50%
        return nonTaxableAmount.add(taxableAmount.divUp(FixedPoint.ONE - swapFeePercentage));
    }

    /*
    Flow of calculations:
    amountsTokenOut -> amountsOutProportional ->
    amountOutPercentageExcess -> amountOutBeforeFee -> newInvariant -> amountBPTIn
    */
    function _calcBptInGivenExactTokensOut(
        uint256 amp,
        uint256[] memory balances,
        uint256[] memory amountsOut,
        uint256 bptTotalSupply,
        uint256 currentInvariant,
        uint256 swapFeePercentage
    ) internal pure returns (uint256) {
        // BPT in, so we round up overall.

        // First loop calculates the sum of all token balances, which will be used to calculate
        // the current weights of each token relative to this sum
        uint256 sumBalances = 0;
        for (uint256 i = 0; i < balances.length; i++) {
            sumBalances = sumBalances.add(balances[i]);
        }

        // Calculate the weighted balance ratio without considering fees
        uint256[] memory balanceRatiosWithoutFee = new uint256[](amountsOut.length);
        uint256 invariantRatioWithoutFees = 0;
        for (uint256 i = 0; i < balances.length; i++) {
            uint256 currentWeight = balances[i].divUp(sumBalances);
            balanceRatiosWithoutFee[i] = balances[i].sub(amountsOut[i]).divUp(balances[i]);
            invariantRatioWithoutFees = invariantRatioWithoutFees.add(balanceRatiosWithoutFee[i].mulUp(currentWeight));
        }

        // Second loop calculates new amounts in, taking into account the fee on the percentage excess
        uint256[] memory newBalances = new uint256[](balances.length);
        for (uint256 i = 0; i < balances.length; i++) {
            // Swap fees are typically charged on 'token in', but there is no 'token in' here, so we apply it to
            // 'token out'. This results in slightly larger price impact.

            uint256 amountOutWithFee;
            if (invariantRatioWithoutFees > balanceRatiosWithoutFee[i]) {
                uint256 nonTaxableAmount = balances[i].mulDown(invariantRatioWithoutFees.complement());
                uint256 taxableAmount = amountsOut[i].sub(nonTaxableAmount);
                // No need to use checked arithmetic for the swap fee, it is guaranteed to be lower than 50%
                amountOutWithFee = nonTaxableAmount.add(taxableAmount.divUp(FixedPoint.ONE - swapFeePercentage));
            } else {
                amountOutWithFee = amountsOut[i];
            }

            newBalances[i] = balances[i].sub(amountOutWithFee);
        }

        uint256 newInvariant = _calculateInvariant(amp, newBalances);
        uint256 invariantRatio = newInvariant.divDown(currentInvariant);

        // return amountBPTIn
        return bptTotalSupply.mulUp(invariantRatio.complement());
    }

    function _calcTokenOutGivenExactBptIn(
        uint256 amp,
        uint256[] memory balances,
        uint256 tokenIndex,
        uint256 bptAmountIn,
        uint256 bptTotalSupply,
        uint256 currentInvariant,
        uint256 swapFeePercentage
    ) internal pure returns (uint256) {
        // Token out, so we round down overall.

        uint256 newInvariant = bptTotalSupply.sub(bptAmountIn).divUp(bptTotalSupply).mulUp(currentInvariant);

        // Calculate amount out without fee
        uint256 newBalanceTokenIndex = _getTokenBalanceGivenInvariantAndAllOtherBalances(
            amp,
            balances,
            newInvariant,
            tokenIndex
        );
        uint256 amountOutWithoutFee = balances[tokenIndex].sub(newBalanceTokenIndex);

        // First calculate the sum of all token balances, which will be used to calculate
        // the current weight of each token
        uint256 sumBalances = 0;
        for (uint256 i = 0; i < balances.length; i++) {
            sumBalances = sumBalances.add(balances[i]);
        }

        // We can now compute how much excess balance is being withdrawn as a result of the virtual swaps, which result
        // in swap fees.
        uint256 currentWeight = balances[tokenIndex].divDown(sumBalances);
        uint256 taxablePercentage = currentWeight.complement();

        // Swap fees are typically charged on 'token in', but there is no 'token in' here, so we apply it
        // to 'token out'. This results in slightly larger price impact. Fees are rounded up.
        uint256 taxableAmount = amountOutWithoutFee.mulUp(taxablePercentage);
        uint256 nonTaxableAmount = amountOutWithoutFee.sub(taxableAmount);

        // No need to use checked arithmetic for the swap fee, it is guaranteed to be lower than 50%
        return nonTaxableAmount.add(taxableAmount.mulDown(FixedPoint.ONE - swapFeePercentage));
    }

    // This function calculates the balance of a given token (tokenIndex)
    // given all the other balances and the invariant
    function _getTokenBalanceGivenInvariantAndAllOtherBalances(
        uint256 amplificationParameter,
        uint256[] memory balances,
        uint256 invariant,
        uint256 tokenIndex
    ) internal pure returns (uint256) {
        // Rounds result up overall

        uint256 ampTimesTotal = amplificationParameter * balances.length;
        uint256 sum = balances[0];
        uint256 P_D = balances[0] * balances.length;
        for (uint256 j = 1; j < balances.length; j++) {
            P_D = Math.divDown(Math.mul(Math.mul(P_D, balances[j]), balances.length), invariant);
            sum = sum.add(balances[j]);
        }
        // No need to use safe math, based on the loop above `sum` is greater than or equal to `balances[tokenIndex]`
        sum = sum - balances[tokenIndex];

        uint256 inv2 = Math.mul(invariant, invariant);
        // We remove the balance from c by multiplying it
        uint256 c = Math.mul(
            Math.mul(Math.divUp(inv2, Math.mul(ampTimesTotal, P_D)), _AMP_PRECISION),
            balances[tokenIndex]
        );
        uint256 b = sum.add(Math.mul(Math.divDown(invariant, ampTimesTotal), _AMP_PRECISION));

        // We iterate to find the balance
        uint256 prevTokenBalance = 0;
        // We multiply the first iteration outside the loop with the invariant to set the value of the
        // initial approximation.
        uint256 tokenBalance = Math.divUp(inv2.add(c), invariant.add(b));

        for (uint256 i = 0; i < 255; i++) {
            prevTokenBalance = tokenBalance;

            tokenBalance = Math.divUp(
                Math.mul(tokenBalance, tokenBalance).add(c),
                Math.mul(tokenBalance, 2).add(b).sub(invariant)
            );

            if (tokenBalance > prevTokenBalance) {
                if (tokenBalance - prevTokenBalance <= 1) {
                    return tokenBalance;
                }
            } else if (prevTokenBalance - tokenBalance <= 1) {
                return tokenBalance;
            }
        }

        _revert(Errors.STABLE_GET_BALANCE_DIDNT_CONVERGE);
    }

    function _computeProportionalAmountsIn(
        uint256[] memory balances,
        uint256 bptAmountOut,
        uint256 totalBPT
    ) internal pure returns (uint256[] memory) {
        /************************************************************************************
        // tokensInForExactBptOut                                                          //
        // (per token)                                                                     //
        // aI = amountIn                   /   bptOut   \                                  //
        // b = balance           aI = b * | ------------ |                                 //
        // bptOut = bptAmountOut           \  totalBPT  /                                  //
        // bpt = totalBPT                                                                  //
        ************************************************************************************/

        // Tokens in, so we round up overall.
        uint256 bptRatio = bptAmountOut.divUp(totalBPT);

        uint256[] memory amountsIn = new uint256[](balances.length);
        for (uint256 i = 0; i < balances.length; i++) {
            amountsIn[i] = balances[i].mulUp(bptRatio);
        }

        return amountsIn;
    }
}

// File: @balancer-labs/v2-solidity-utils/contracts/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 "@balancer-labs/v2-interfaces/contracts/solidity-utils/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 >> 255 == 0, 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: @balancer-labs/v2-interfaces/contracts/vault/IGeneralPool.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 IPools with the General specialization setting 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 IGeneralPool is IBasePool {
    function onSwap(
        SwapRequest memory swapRequest,
        uint256[] memory balances,
        uint256 indexIn,
        uint256 indexOut
    ) external returns (uint256 amount);
}

// File: @balancer-labs/v2-pool-utils/contracts/BasePool.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 "@balancer-labs/v2-interfaces/contracts/pool-utils/IAssetManager.sol";
import "@balancer-labs/v2-interfaces/contracts/pool-utils/IControlledPool.sol";
import "@balancer-labs/v2-interfaces/contracts/vault/IVault.sol";
import "@balancer-labs/v2-interfaces/contracts/vault/IBasePool.sol";

import "@balancer-labs/v2-solidity-utils/contracts/helpers/InputHelpers.sol";
import "@balancer-labs/v2-solidity-utils/contracts/helpers/WordCodec.sol";
import "@balancer-labs/v2-solidity-utils/contracts/helpers/TemporarilyPausable.sol";
import "@balancer-labs/v2-solidity-utils/contracts/openzeppelin/ERC20.sol";
import "@balancer-labs/v2-solidity-utils/contracts/math/FixedPoint.sol";
import "@balancer-labs/v2-solidity-utils/contracts/math/Math.sol";

import "./BalancerPoolToken.sol";
import "./BasePoolAuthorization.sol";
import "./RecoveryMode.sol";

// solhint-disable max-states-count

/**
 * @notice Reference implementation for the base layer of a Pool contract.
 * @dev Reference implementation for the base layer of a Pool contract that manages a single Pool with optional
 * Asset Managers, an admin-controlled swap fee percentage, and an emergency pause mechanism.
 *
 * This Pool pays protocol fees by minting BPT directly to the ProtocolFeeCollector instead of using the
 * `dueProtocolFees` return value. This results in the underlying tokens continuing to provide liquidity
 * for traders, while still keeping gas usage to a minimum since only a single token (the BPT) is transferred.
 *
 * Note that neither swap fees nor the pause mechanism are used by this contract. They are passed through so that
 * derived contracts can use them via the `_addSwapFeeAmount` and `_subtractSwapFeeAmount` functions, and the
 * `whenNotPaused` modifier.
 *
 * No admin permissions are checked here: instead, this contract delegates that to the Vault's own Authorizer.
 *
 * Because this contract doesn't implement the swap hooks, derived contracts should generally inherit from
 * BaseGeneralPool or BaseMinimalSwapInfoPool. Otherwise, subclasses must inherit from the corresponding interfaces
 * and implement the swap callbacks themselves.
 */
abstract contract BasePool is
    IBasePool,
    IControlledPool,
    BasePoolAuthorization,
    BalancerPoolToken,
    TemporarilyPausable,
    RecoveryMode
{
    using WordCodec for bytes32;
    using FixedPoint for uint256;
    using BasePoolUserData for bytes;

    uint256 private constant _MIN_TOKENS = 2;

    uint256 private constant _DEFAULT_MINIMUM_BPT = 1e6;

    // 1e18 corresponds to 1.0, or a 100% fee
    uint256 private constant _MIN_SWAP_FEE_PERCENTAGE = 1e12; // 0.0001%
    uint256 private constant _MAX_SWAP_FEE_PERCENTAGE = 1e17; // 10% - this fits in 64 bits

    // `_miscData` is a storage slot that can be used to store unrelated pieces of information. All pools store the
    // recovery mode flag and swap fee percentage, but `miscData` can be extended to store more pieces of information.
    // The most signficant bit is reserved for the recovery mode flag, and the swap fee percentage is stored in
    // the next most significant 63 bits, leaving the remaining 192 bits free to store any other information derived
    // pools might need.
    //
    // This slot is preferred for gas-sensitive operations as it is read in all joins, swaps and exits,
    // and therefore warm.

    // [ recovery | swap  fee | available ]
    // [   1 bit  |  63 bits  |  192 bits ]
    // [ MSB                          LSB ]
    bytes32 private _miscData;

    uint256 private constant _SWAP_FEE_PERCENTAGE_OFFSET = 192;
    uint256 private constant _RECOVERY_MODE_BIT_OFFSET = 255;

    // A fee can never be larger than FixedPoint.ONE, which fits in 60 bits, so 63 is more than enough.
    uint256 private constant _SWAP_FEE_PERCENTAGE_BIT_LENGTH = 63;

    bytes32 private immutable _poolId;

    // Note that this value is immutable in the Vault, so we can make it immutable here and save gas
    IProtocolFeesCollector private immutable _protocolFeesCollector;

    event SwapFeePercentageChanged(uint256 swapFeePercentage);

    constructor(
        IVault vault,
        IVault.PoolSpecialization specialization,
        string memory name,
        string memory symbol,
        IERC20[] memory tokens,
        address[] memory assetManagers,
        uint256 swapFeePercentage,
        uint256 pauseWindowDuration,
        uint256 bufferPeriodDuration,
        address owner
    )
        // Base Pools are expected to be deployed using factories. By using the factory address as the action
        // disambiguator, we make all Pools deployed by the same factory share action identifiers. This allows for
        // simpler management of permissions (such as being able to manage granting the 'set fee percentage' action in
        // any Pool created by the same factory), while still making action identifiers unique among different factories
        // if the selectors match, preventing accidental errors.
        Authentication(bytes32(uint256(msg.sender)))
        BalancerPoolToken(name, symbol, vault)
        BasePoolAuthorization(owner)
        TemporarilyPausable(pauseWindowDuration, bufferPeriodDuration)
    {
        _require(tokens.length >= _MIN_TOKENS, Errors.MIN_TOKENS);
        _require(tokens.length <= _getMaxTokens(), Errors.MAX_TOKENS);

        // The Vault only requires the token list to be ordered for the Two Token Pools specialization. However,
        // to make the developer experience consistent, we are requiring this condition for all the native pools.
        // Also, since these Pools will register tokens only once, we can ensure the Pool tokens will follow the same
        // order. We rely on this property to make Pools simpler to write, as it lets us assume that the
        // order of token-specific parameters (such as token weights) will not change.
        InputHelpers.ensureArrayIsSorted(tokens);

        _setSwapFeePercentage(swapFeePercentage);

        bytes32 poolId = vault.registerPool(specialization);

        vault.registerTokens(poolId, tokens, assetManagers);

        // Set immutable state variables - these cannot be read from during construction
        _poolId = poolId;
        _protocolFeesCollector = vault.getProtocolFeesCollector();
    }

    // Getters / Setters

    /**
     * @notice Return the pool id.
     */
    function getPoolId() public view override returns (bytes32) {
        return _poolId;
    }

    function _getTotalTokens() internal view virtual returns (uint256);

    function _getMaxTokens() internal pure virtual returns (uint256);

    /**
     * @dev Returns the minimum BPT supply. This amount is minted to the zero address during initialization, effectively
     * locking it.
     *
     * This is useful to make sure Pool initialization happens only once, but derived Pools can change this value (even
     * to zero) by overriding this function.
     */
    function _getMinimumBpt() internal pure virtual returns (uint256) {
        return _DEFAULT_MINIMUM_BPT;
    }

    /**
     * @notice Return the current value of the swap fee percentage.
     * @dev This is stored in `_miscData`.
     */
    function getSwapFeePercentage() public view virtual override returns (uint256) {
        return _miscData.decodeUint(_SWAP_FEE_PERCENTAGE_OFFSET, _SWAP_FEE_PERCENTAGE_BIT_LENGTH);
    }

    /**
     * @notice Return the ProtocolFeesCollector contract.
     * @dev This is immutable, and retrieved from the Vault on construction. (It is also immutable in the Vault.)
     */
    function getProtocolFeesCollector() public view returns (IProtocolFeesCollector) {
        return _protocolFeesCollector;
    }

    /**
     * @notice Set the swap fee percentage.
     * @dev This is a permissioned function, and disabled if the pool is paused. The swap fee must be within the
     * bounds set by MIN_SWAP_FEE_PERCENTAGE/MAX_SWAP_FEE_PERCENTAGE. Emits the SwapFeePercentageChanged event.
     */
    function setSwapFeePercentage(uint256 swapFeePercentage) public virtual override authenticate whenNotPaused {
        _setSwapFeePercentage(swapFeePercentage);
    }

    function _setSwapFeePercentage(uint256 swapFeePercentage) internal virtual {
        _require(swapFeePercentage >= _getMinSwapFeePercentage(), Errors.MIN_SWAP_FEE_PERCENTAGE);
        _require(swapFeePercentage <= _getMaxSwapFeePercentage(), Errors.MAX_SWAP_FEE_PERCENTAGE);

        _miscData = _miscData.insertUint(
            swapFeePercentage,
            _SWAP_FEE_PERCENTAGE_OFFSET,
            _SWAP_FEE_PERCENTAGE_BIT_LENGTH
        );

        emit SwapFeePercentageChanged(swapFeePercentage);
    }

    function _getMinSwapFeePercentage() internal pure virtual returns (uint256) {
        return _MIN_SWAP_FEE_PERCENTAGE;
    }

    function _getMaxSwapFeePercentage() internal pure virtual returns (uint256) {
        return _MAX_SWAP_FEE_PERCENTAGE;
    }

    /**
     * @notice Returns whether the pool is in Recovery Mode.
     */
    function inRecoveryMode() public view override returns (bool) {
        return _miscData.decodeBool(_RECOVERY_MODE_BIT_OFFSET);
    }

    /**
     * @dev Sets the recoveryMode state, and emits the corresponding event.
     */
    function _setRecoveryMode(bool enabled) internal virtual override {
        _miscData = _miscData.insertBool(enabled, _RECOVERY_MODE_BIT_OFFSET);

        emit RecoveryModeStateChanged(enabled);

        // Some pools need to update their state when leaving recovery mode to ensure proper functioning of the Pool.
        // We do not allow an `_onEnableRecoveryMode()` hook as this may jeopardize the ability to enable Recovery mode.
        if (!enabled) _onDisableRecoveryMode();
    }

    /**
     * @dev Performs any necessary actions on the disabling of Recovery Mode.
     * This is usually to reset any fee collection mechanisms to ensure that they operate correctly going forward.
     */
    function _onDisableRecoveryMode() internal virtual {}

    /**
     * @notice Set the asset manager parameters for the given token.
     * @dev This is a permissioned function, unavailable when the pool is paused.
     * The details of the configuration data are set by each Asset Manager. (For an example, see
     * `RewardsAssetManager`.)
     */
    function setAssetManagerPoolConfig(IERC20 token, bytes memory poolConfig)
        public
        virtual
        override
        authenticate
        whenNotPaused
    {
        _setAssetManagerPoolConfig(token, poolConfig);
    }

    function _setAssetManagerPoolConfig(IERC20 token, bytes memory poolConfig) private {
        bytes32 poolId = getPoolId();
        (, , , address assetManager) = getVault().getPoolTokenInfo(poolId, token);

        IAssetManager(assetManager).setConfig(poolId, poolConfig);
    }

    /**
     * @notice Pause the pool: an emergency action which disables all pool functions.
     * @dev This is a permissioned function that will only work during the Pause Window set during pool factory
     * deployment (see `TemporarilyPausable`).
     */
    function pause() external authenticate {
        _setPaused(true);
    }

    /**
     * @notice Reverse a `pause` operation, and restore a pool to normal functionality.
     * @dev This is a permissioned function that will only work on a paused pool within the Buffer Period set during
     * pool factory deployment (see `TemporarilyPausable`). Note that any paused pools will automatically unpause
     * after the Buffer Period expires.
     */
    function unpause() external authenticate {
        _setPaused(false);
    }

    function _isOwnerOnlyAction(bytes32 actionId) internal view virtual override returns (bool) {
        return
            (actionId == getActionId(this.setSwapFeePercentage.selector)) ||
            (actionId == getActionId(this.setAssetManagerPoolConfig.selector)) ||
            super._isOwnerOnlyAction(actionId);
    }

    function _getMiscData() internal view returns (bytes32) {
        return _miscData;
    }

    /**
     * @dev Inserts data into the least-significant 192 bits of the misc data storage slot.
     * Note that the remaining 64 bits are used for the swap fee percentage and cannot be overloaded.
     */
    function _setMiscData(bytes32 newData) internal {
        _miscData = _miscData.insertBits192(newData, 0);
    }

    // Join / Exit Hooks

    modifier onlyVault(bytes32 poolId) {
        _require(msg.sender == address(getVault()), Errors.CALLER_NOT_VAULT);
        _require(poolId == getPoolId(), Errors.INVALID_POOL_ID);
        _;
    }

    /**
     * @notice Vault hook for adding liquidity to a pool (including the first time, "initializing" the pool).
     * @dev This function can only be called from the Vault, from `joinPool`.
     */
    function onJoinPool(
        bytes32 poolId,
        address sender,
        address recipient,
        uint256[] memory balances,
        uint256 lastChangeBlock,
        uint256 protocolSwapFeePercentage,
        bytes memory userData
    ) external override onlyVault(poolId) returns (uint256[] memory, uint256[] memory) {
        _beforeSwapJoinExit();

        uint256[] memory scalingFactors = _scalingFactors();

        if (totalSupply() == 0) {
            (uint256 bptAmountOut, uint256[] memory amountsIn) = _onInitializePool(
                poolId,
                sender,
                recipient,
                scalingFactors,
                userData
            );

            // On initialization, we lock _getMinimumBpt() by minting it for the zero address. This BPT acts as a
            // minimum as it will never be burned, which reduces potential issues with rounding, and also prevents the
            // Pool from ever being fully drained.
            _require(bptAmountOut >= _getMinimumBpt(), Errors.MINIMUM_BPT);
            _mintPoolTokens(address(0), _getMinimumBpt());
            _mintPoolTokens(recipient, bptAmountOut - _getMinimumBpt());

            // amountsIn are amounts entering the Pool, so we round up.
            _downscaleUpArray(amountsIn, scalingFactors);

            return (amountsIn, new uint256[](balances.length));
        } else {
            _upscaleArray(balances, scalingFactors);
            (uint256 bptAmountOut, uint256[] memory amountsIn) = _onJoinPool(
                poolId,
                sender,
                recipient,
                balances,
                lastChangeBlock,
                inRecoveryMode() ? 0 : protocolSwapFeePercentage, // Protocol fees are disabled while in recovery mode
                scalingFactors,
                userData
            );

            // Note we no longer use `balances` after calling `_onJoinPool`, which may mutate it.

            _mintPoolTokens(recipient, bptAmountOut);

            // amountsIn are amounts entering the Pool, so we round up.
            _downscaleUpArray(amountsIn, scalingFactors);

            // This Pool ignores the `dueProtocolFees` return value, so we simply return a zeroed-out array.
            return (amountsIn, new uint256[](balances.length));
        }
    }

    /**
     * @notice Vault hook for removing liquidity from a pool.
     * @dev This function can only be called from the Vault, from `exitPool`.
     */
    function onExitPool(
        bytes32 poolId,
        address sender,
        address recipient,
        uint256[] memory balances,
        uint256 lastChangeBlock,
        uint256 protocolSwapFeePercentage,
        bytes memory userData
    ) external override onlyVault(poolId) returns (uint256[] memory, uint256[] memory) {
        uint256[] memory amountsOut;
        uint256 bptAmountIn;

        // When a user calls `exitPool`, this is the first point of entry from the Vault.
        // We first check whether this is a Recovery Mode exit - if so, we proceed using this special lightweight exit
        // mechanism which avoids computing any complex values, interacting with external contracts, etc., and generally
        // should always work, even if the Pool's mathematics or a dependency break down.
        if (userData.isRecoveryModeExitKind()) {
            // This exit kind is only available in Recovery Mode.
            _ensureInRecoveryMode();

            // Note that we don't upscale balances nor downscale amountsOut - we don't care about scaling factors during
            // a recovery mode exit.
            (bptAmountIn, amountsOut) = _doRecoveryModeExit(balances, totalSupply(), userData);
        } else {
            // Note that we only call this if we're not in a recovery mode exit.
            _beforeSwapJoinExit();

            uint256[] memory scalingFactors = _scalingFactors();
            _upscaleArray(balances, scalingFactors);

            (bptAmountIn, amountsOut) = _onExitPool(
                poolId,
                sender,
                recipient,
                balances,
                lastChangeBlock,
                inRecoveryMode() ? 0 : protocolSwapFeePercentage, // Protocol fees are disabled while in recovery mode
                scalingFactors,
                userData
            );

            // amountsOut are amounts exiting the Pool, so we round down.
            _downscaleDownArray(amountsOut, scalingFactors);
        }

        // Note we no longer use `balances` after calling `_onExitPool`, which may mutate it.

        _burnPoolTokens(sender, bptAmountIn);

        // This Pool ignores the `dueProtocolFees` return value, so we simply return a zeroed-out array.
        return (amountsOut, new uint256[](balances.length));
    }

    // Query functions

    /**
     * @notice "Dry run" `onJoinPool`.
     * @dev Returns the amount of BPT that would be granted to `recipient` if the `onJoinPool` hook were called by the
     * Vault with the same arguments, along with the number of tokens `sender` would have to supply.
     *
     * This function is not meant to be called directly, but rather from a helper contract that fetches current Vault
     * data, such as the protocol swap fee percentage and Pool balances.
     *
     * Like `IVault.queryBatchSwap`, this function is not view due to internal implementation details: the caller must
     * explicitly use eth_call instead of eth_sendTransaction.
     */
    function queryJoin(
        bytes32 poolId,
        address sender,
        address recipient,
        uint256[] memory balances,
        uint256 lastChangeBlock,
        uint256 protocolSwapFeePercentage,
        bytes memory userData
    ) external override returns (uint256 bptOut, uint256[] memory amountsIn) {
        InputHelpers.ensureInputLengthMatch(balances.length, _getTotalTokens());

        _queryAction(
            poolId,
            sender,
            recipient,
            balances,
            lastChangeBlock,
            protocolSwapFeePercentage,
            userData,
            _onJoinPool,
            _downscaleUpArray
        );

        // The `return` opcode is executed directly inside `_queryAction`, so execution never reaches this statement,
        // and we don't need to return anything here - it just silences compiler warnings.
        return (bptOut, amountsIn);
    }

    /**
     * @notice "Dry run" `onExitPool`.
     * @dev Returns the amount of BPT that would be burned from `sender` if the `onExitPool` hook were called by the
     * Vault with the same arguments, along with the number of tokens `recipient` would receive.
     *
     * This function is not meant to be called directly, but rather from a helper contract that fetches current Vault
     * data, such as the protocol swap fee percentage and Pool balances.
     *
     * Like `IVault.queryBatchSwap`, this function is not view due to internal implementation details: the caller must
     * explicitly use eth_call instead of eth_sendTransaction.
     */
    function queryExit(
        bytes32 poolId,
        address sender,
        address recipient,
        uint256[] memory balances,
        uint256 lastChangeBlock,
        uint256 protocolSwapFeePercentage,
        bytes memory userData
    ) external override returns (uint256 bptIn, uint256[] memory amountsOut) {
        InputHelpers.ensureInputLengthMatch(balances.length, _getTotalTokens());

        _queryAction(
            poolId,
            sender,
            recipient,
            balances,
            lastChangeBlock,
            protocolSwapFeePercentage,
            userData,
            _onExitPool,
            _downscaleDownArray
        );

        // The `return` opcode is executed directly inside `_queryAction`, so execution never reaches this statement,
        // and we don't need to return anything here - it just silences compiler warnings.
        return (bptIn, amountsOut);
    }

    // Internal hooks to be overridden by derived contracts - all token amounts (except BPT) in these interfaces are
    // upscaled.

    /**
     * @dev Called when the Pool is joined for the first time; that is, when the BPT total supply is zero.
     *
     * Returns the amount of BPT to mint, and the token amounts the Pool will receive in return.
     *
     * Minted BPT will be sent to `recipient`, except for _getMinimumBpt(), which will be deducted from this amount and
     * sent to the zero address instead. This will cause that BPT to remain forever locked there, preventing total BTP
     * from ever dropping below that value, and ensuring `_onInitializePool` can only be called once in the entire
     * Pool's lifetime.
     *
     * The tokens granted to the Pool will be transferred from `sender`. These amounts are considered upscaled and will
     * be downscaled (rounding up) before being returned to the Vault.
     */
    function _onInitializePool(
        bytes32 poolId,
        address sender,
        address recipient,
        uint256[] memory scalingFactors,
        bytes memory userData
    ) internal virtual returns (uint256 bptAmountOut, uint256[] memory amountsIn);

    /**
     * @dev Called whenever the Pool is joined after the first initialization join (see `_onInitializePool`).
     *
     * Returns the amount of BPT to mint, the token amounts that the Pool will receive in return, and the number of
     * tokens to pay in protocol swap fees.
     *
     * Implementations of this function might choose to mutate the `balances` array to save gas (e.g. when
     * performing intermediate calculations, such as subtraction of due protocol fees). This can be done safely.
     *
     * Minted BPT will be sent to `recipient`.
     *
     * The tokens granted to the Pool will be transferred from `sender`. These amounts are considered upscaled and will
     * be downscaled (rounding up) before being returned to the Vault.
     *
     * Due protocol swap fees will be taken from the Pool's balance in the Vault (see `IBasePool.onJoinPool`). These
     * amounts are considered upscaled and will be downscaled (rounding down) before being returned to the Vault.
     */
    function _onJoinPool(
        bytes32 poolId,
        address sender,
        address recipient,
        uint256[] memory balances,
        uint256 lastChangeBlock,
        uint256 protocolSwapFeePercentage,
        uint256[] memory scalingFactors,
        bytes memory userData
    ) internal virtual returns (uint256 bptAmountOut, uint256[] memory amountsIn);

    /**
     * @dev Called whenever the Pool is exited.
     *
     * Returns the amount of BPT to burn, the token amounts for each Pool token that the Pool will grant in return, and
     * the number of tokens to pay in protocol swap fees.
     *
     * Implementations of this function might choose to mutate the `balances` array to save gas (e.g. when
     * performing intermediate calculations, such as subtraction of due protocol fees). This can be done safely.
     *
     * BPT will be burnt from `sender`.
     *
     * The Pool will grant tokens to `recipient`. These amounts are considered upscaled and will be downscaled
     * (rounding down) before being returned to the Vault.
     *
     * Due protocol swap fees will be taken from the Pool's balance in the Vault (see `IBasePool.onExitPool`). These
     * amounts are considered upscaled and will be downscaled (rounding down) before being returned to the Vault.
     */
    function _onExitPool(
        bytes32 poolId,
        address sender,
        address recipient,
        uint256[] memory balances,
        uint256 lastChangeBlock,
        uint256 protocolSwapFeePercentage,
        uint256[] memory scalingFactors,
        bytes memory userData
    ) internal virtual returns (uint256 bptAmountIn, uint256[] memory amountsOut);

    /**
     * @dev Called at the very beginning of swaps, joins and exits, even before the scaling factors are read. Derived
     * contracts can extend this implementation to perform any state-changing operations they might need (including e.g.
     * updating the scaling factors),
     *
     * The only scenario in which this function is not called is during a recovery mode exit. This makes it safe to
     * perform non-trivial computations or interact with external dependencies here, as recovery mode will not be
     * affected.
     *
     * Since this contract does not implement swaps, derived contracts must also make sure this function is called on
     * swap handlers.
     */
    function _beforeSwapJoinExit() internal virtual {
        // All joins, exits and swaps are disabled (except recovery mode exits).
        _ensureNotPaused();
    }

    // Internal functions

    /**
     * @dev Pays protocol fees by minting `bptAmount` to the Protocol Fee Collector.
     */
    function _payProtocolFees(uint256 bptAmount) internal {
        _mintPoolTokens(address(getProtocolFeesCollector()), bptAmount);
    }

    /**
     * @dev Adds swap fee amount to `amount`, returning a higher value.
     */
    function _addSwapFeeAmount(uint256 amount) internal view returns (uint256) {
        // This returns amount + fee amount, so we round up (favoring a higher fee amount).
        return amount.divUp(getSwapFeePercentage().complement());
    }

    /**
     * @dev Subtracts swap fee amount from `amount`, returning a lower value.
     */
    function _subtractSwapFeeAmount(uint256 amount) internal view returns (uint256) {
        // This returns amount - fee amount, so we round up (favoring a higher fee amount).
        uint256 feeAmount = amount.mulUp(getSwapFeePercentage());
        return amount.sub(feeAmount);
    }

    // Scaling

    /**
     * @dev Returns a scaling factor that, when multiplied to a token amount for `token`, normalizes its balance as if
     * it had 18 decimals.
     */
    function _computeScalingFactor(IERC20 token) internal view returns (uint256) {
        if (address(token) == address(this)) {
            return FixedPoint.ONE;
        }

        // Tokens that don't implement the `decimals` method are not supported.
        uint256 tokenDecimals = ERC20(address(token)).decimals();

        // Tokens with more than 18 decimals are not supported.
        uint256 decimalsDifference = Math.sub(18, tokenDecimals);
        return FixedPoint.ONE * 10**decimalsDifference;
    }

    /**
     * @dev Returns the scaling factor for one of the Pool's tokens. Reverts if `token` is not a token registered by the
     * Pool.
     *
     * All scaling factors are fixed-point values with 18 decimals, to allow for this function to be overridden by
     * derived contracts that need to apply further scaling, making these factors potentially non-integer.
     *
     * The largest 'base' scaling factor (i.e. in tokens with less than 18 decimals) is 10**18, which in fixed-point is
     * 10**36. This value can be multiplied with a 112 bit Vault balance with no overflow by a factor of ~1e7, making
     * even relatively 'large' factors safe to use.
     *
     * The 1e7 figure is the result of 2**256 / (1e18 * 1e18 * 2**112).
     */
    function _scalingFactor(IERC20 token) internal view virtual returns (uint256);

    /**
     * @dev Same as `_scalingFactor()`, except for all registered tokens (in the same order as registered). The Vault
     * will always pass balances in this order when calling any of the Pool hooks.
     */
    function _scalingFactors() internal view virtual returns (uint256[] memory);

    function getScalingFactors() external view override returns (uint256[] memory) {
        return _scalingFactors();
    }

    /**
     * @dev Applies `scalingFactor` to `amount`, resulting in a larger or equal value depending on whether it needed
     * scaling or not.
     */
    function _upscale(uint256 amount, uint256 scalingFactor) internal pure returns (uint256) {
        // Upscale rounding wouldn't necessarily always go in the same direction: in a swap for example the balance of
        // token in should be rounded up, and that of token out rounded down. This is the only place where we round in
        // the same direction for all amounts, as the impact of this rounding is expected to be minimal (and there's no
        // rounding error unless `_scalingFactor()` is overriden).
        return FixedPoint.mulDown(amount, scalingFactor);
    }

    /**
     * @dev Same as `_upscale`, but for an entire array. This function does not return anything, but instead *mutates*
     * the `amounts` array.
     */
    function _upscaleArray(uint256[] memory amounts, uint256[] memory scalingFactors) internal pure {
        uint256 length = amounts.length;
        InputHelpers.ensureInputLengthMatch(length, scalingFactors.length);

        for (uint256 i = 0; i < length; ++i) {
            amounts[i] = FixedPoint.mulDown(amounts[i], scalingFactors[i]);
        }
    }

    /**
     * @dev Reverses the `scalingFactor` applied to `amount`, resulting in a smaller or equal value depending on
     * whether it needed scaling or not. The result is rounded down.
     */
    function _downscaleDown(uint256 amount, uint256 scalingFactor) internal pure returns (uint256) {
        return FixedPoint.divDown(amount, scalingFactor);
    }

    /**
     * @dev Same as `_downscaleDown`, but for an entire array. This function does not return anything, but instead
     * *mutates* the `amounts` array.
     */
    function _downscaleDownArray(uint256[] memory amounts, uint256[] memory scalingFactors) internal pure {
        uint256 length = amounts.length;
        InputHelpers.ensureInputLengthMatch(length, scalingFactors.length);

        for (uint256 i = 0; i < length; ++i) {
            amounts[i] = FixedPoint.divDown(amounts[i], scalingFactors[i]);
        }
    }

    /**
     * @dev Reverses the `scalingFactor` applied to `amount`, resulting in a smaller or equal value depending on
     * whether it needed scaling or not. The result is rounded up.
     */
    function _downscaleUp(uint256 amount, uint256 scalingFactor) internal pure returns (uint256) {
        return FixedPoint.divUp(amount, scalingFactor);
    }

    /**
     * @dev Same as `_downscaleUp`, but for an entire array. This function does not return anything, but instead
     * *mutates* the `amounts` array.
     */
    function _downscaleUpArray(uint256[] memory amounts, uint256[] memory scalingFactors) internal pure {
        uint256 length = amounts.length;
        InputHelpers.ensureInputLengthMatch(length, scalingFactors.length);

        for (uint256 i = 0; i < length; ++i) {
            amounts[i] = FixedPoint.divUp(amounts[i], scalingFactors[i]);
        }
    }

    function _getAuthorizer() internal view override returns (IAuthorizer) {
        // Access control management is delegated to the Vault's Authorizer. This lets Balancer Governance manage which
        // accounts can call permissioned functions: for example, to perform emergency pauses.
        // If the owner is delegated, then *all* permissioned functions, including `setSwapFeePercentage`, will be under
        // Governance control.
        return getVault().getAuthorizer();
    }

    function _queryAction(
        bytes32 poolId,
        address sender,
        address recipient,
        uint256[] memory balances,
        uint256 lastChangeBlock,
        uint256 protocolSwapFeePercentage,
        bytes memory userData,
        function(bytes32, address, address, uint256[] memory, uint256, uint256, uint256[] memory, bytes memory)
            internal
            returns (uint256, uint256[] memory) _action,
        function(uint256[] memory, uint256[] memory) internal view _downscaleArray
    ) private {
        // This uses the same technique used by the Vault in queryBatchSwap. Refer to that function for a detailed
        // explanation.

        if (msg.sender != address(this)) {
            // We perform an external call to ourselves, forwarding the same calldata. In this call, the else clause of
            // the preceding if statement will be executed instead.

            // solhint-disable-next-line avoid-low-level-calls
            (bool success, ) = address(this).call(msg.data);

            // solhint-disable-next-line no-inline-assembly
            assembly {
                // This call should always revert to decode the bpt and token amounts from the revert reason
                switch success
                    case 0 {
                        // Note we are manually writing the memory slot 0. We can safely overwrite whatever is
                        // stored there as we take full control of the execution and then immediately return.

                        // We copy the first 4 bytes to check if it matches with the expected signature, otherwise
                        // there was another revert reason and we should forward it.
                        returndatacopy(0, 0, 0x04)
                        let error := and(mload(0), 0xffffffff00000000000000000000000000000000000000000000000000000000)

                        // If the first 4 bytes don't match with the expected signature, we forward the revert reason.
                        if eq(eq(error, 0x43adbafb00000000000000000000000000000000000000000000000000000000), 0) {
                            returndatacopy(0, 0, returndatasize())
                            revert(0, returndatasize())
                        }

                        // The returndata contains the signature, followed by the raw memory representation of the
                        // `bptAmount` and `tokenAmounts` (array: length + data). We need to return an ABI-encoded
                        // representation of these.
                        // An ABI-encoded response will include one additional field to indicate the starting offset of
                        // the `tokenAmounts` array. The `bptAmount` will be laid out in the first word of the
                        // returndata.
                        //
                        // In returndata:
                        // [ signature ][ bptAmount ][ tokenAmounts length ][ tokenAmounts values ]
                        // [  4 bytes  ][  32 bytes ][       32 bytes      ][ (32 * length) bytes ]
                        //
                        // We now need to return (ABI-encoded values):
                        // [ bptAmount ][ tokeAmounts offset ][ tokenAmounts length ][ tokenAmounts values ]
                        // [  32 bytes ][       32 bytes     ][       32 bytes      ][ (32 * length) bytes ]

                        // We copy 32 bytes for the `bptAmount` from returndata into memory.
                        // Note that we skip the first 4 bytes for the error signature
                        returndatacopy(0, 0x04, 32)

                        // The offsets are 32-bytes long, so the array of `tokenAmounts` will start after
                        // the initial 64 bytes.
                        mstore(0x20, 64)

                        // We now copy the raw memory array for the `tokenAmounts` from returndata into memory.
                        // Since bpt amount and offset take up 64 bytes, we start copying at address 0x40. We also
                        // skip the first 36 bytes from returndata, which correspond to the signature plus bpt amount.
                        returndatacopy(0x40, 0x24, sub(returndatasize(), 36))

                        // We finally return the ABI-encoded uint256 and the array, which has a total length equal to
                        // the size of returndata, plus the 32 bytes of the offset but without the 4 bytes of the
                        // error signature.
                        return(0, add(returndatasize(), 28))
                    }
                    default {
                        // This call should always revert, but we fail nonetheless if that didn't happen
                        invalid()
                    }
            }
        } else {
            // This imitates the relevant parts of the bodies of onJoin and onExit. Since they're not virtual, we know
            // that their implementations will match this regardless of what derived contracts might do.

            _beforeSwapJoinExit();

            uint256[] memory scalingFactors = _scalingFactors();
            _upscaleArray(balances, scalingFactors);

            (uint256 bptAmount, uint256[] memory tokenAmounts) = _action(
                poolId,
                sender,
                recipient,
                balances,
                lastChangeBlock,
                protocolSwapFeePercentage,
                scalingFactors,
                userData
            );

            _downscaleArray(tokenAmounts, scalingFactors);

            // solhint-disable-next-line no-inline-assembly
            assembly {
                // We will return a raw representation of `bptAmount` and `tokenAmounts` in memory, which is composed of
                // a 32-byte uint256, followed by a 32-byte for the array length, and finally the 32-byte uint256 values
                // Because revert expects a size in bytes, we multiply the array length (stored at `tokenAmounts`) by 32
                let size := mul(mload(tokenAmounts), 32)

                // We store the `bptAmount` in the previous slot to the `tokenAmounts` array. We can make sure there
                // will be at least one available slot due to how the memory scratch space works.
                // We can safely overwrite whatever is stored in this slot as we will revert immediately after that.
                let start := sub(tokenAmounts, 0x20)
                mstore(start, bptAmount)

                // We send one extra value for the error signature "QueryError(uint256,uint256[])" which is 0x43adbafb
                // We use the previous slot to `bptAmount`.
                mstore(sub(start, 0x20), 0x0000000000000000000000000000000000000000000000000000000043adbafb)
                start := sub(start, 0x04)

                // When copying from `tokenAmounts` into returndata, we copy the additional 68 bytes to also return
                // the `bptAmount`, the array 's length, and the error signature.
                revert(start, add(size, 68))
            }
        }
    }
}

// File: @balancer-labs/v2-interfaces/contracts/vault/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). `balances` 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. `balances` 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);

    /**
     * @dev Returns this Pool's ID, used when interacting with the Vault (to e.g. join the Pool or swap with it).
     */
    function getPoolId() external view returns (bytes32);

    /**
     * @dev Returns the current swap fee percentage as a 18 decimal fixed point number, so e.g. 1e17 corresponds to a
     * 10% swap fee.
     */
    function getSwapFeePercentage() external view returns (uint256);

    /**
     * @dev Returns the scaling factors of each of the Pool's tokens. This is an implementation detail that is typically
     * not relevant for outside parties, but which might be useful for some types of Pools.
     */
    function getScalingFactors() external view returns (uint256[] memory);

    function queryJoin(
        bytes32 poolId,
        address sender,
        address recipient,
        uint256[] memory balances,
        uint256 lastChangeBlock,
        uint256 protocolSwapFeePercentage,
        bytes memory userData
    ) external returns (uint256 bptOut, uint256[] memory amountsIn);

    function queryExit(
        bytes32 poolId,
        address sender,
        address recipient,
        uint256[] memory balances,
        uint256 lastChangeBlock,
        uint256 protocolSwapFeePercentage,
        bytes memory userData
    ) external returns (uint256 bptIn, uint256[] memory amountsOut);
}

// File: @balancer-labs/v2-interfaces/contracts/vault/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 "../solidity-utils/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: @balancer-labs/v2-interfaces/contracts/pool-utils/IAssetManager.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 "../solidity-utils/openzeppelin/IERC20.sol";

interface IAssetManager {
    /**
     * @notice Emitted when asset manager is rebalanced
     */
    event Rebalance(bytes32 poolId);

    /**
     * @notice Sets the config
     */
    function setConfig(bytes32 poolId, bytes calldata config) external;

    /**
     * Note: No function to read the asset manager config is included in IAssetManager
     * as the signature is expected to vary between asset manager implementations
     */

    /**
     * @notice Returns the asset manager's token
     */
    function getToken() external view returns (IERC20);

    /**
     * @return the current assets under management of this asset manager
     */
    function getAUM(bytes32 poolId) external view returns (uint256);

    /**
     * @return poolCash - The up-to-date cash balance of the pool
     * @return poolManaged - The up-to-date managed balance of the pool
     */
    function getPoolBalances(bytes32 poolId) external view returns (uint256 poolCash, uint256 poolManaged);

    /**
     * @return The difference in tokens between the target investment
     * and the currently invested amount (i.e. the amount that can be invested)
     */
    function maxInvestableBalance(bytes32 poolId) external view returns (int256);

    /**
     * @notice Updates the Vault on the value of the pool's investment returns
     */
    function updateBalanceOfPool(bytes32 poolId) external;

    /**
     * @notice Determines whether the pool should rebalance given the provided balances
     */
    function shouldRebalance(uint256 cash, uint256 managed) external view returns (bool);

    /**
     * @notice Rebalances funds between the pool and the asset manager to maintain target investment percentage.
     * @param poolId - the poolId of the pool to be rebalanced
     * @param force - a boolean representing whether a rebalance should be forced even when the pool is near balance
     */
    function rebalance(bytes32 poolId, bool force) external;

    /**
     * @notice allows an authorized rebalancer to remove capital to facilitate large withdrawals
     * @param poolId - the poolId of the pool to withdraw funds back to
     * @param amount - the amount of tokens to withdraw back to the pool
     */
    function capitalOut(bytes32 poolId, uint256 amount) external;
}

// File: @balancer-labs/v2-interfaces/contracts/pool-utils/IControlledPool.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 "../solidity-utils/openzeppelin/IERC20.sol";

interface IControlledPool {
    function setSwapFeePercentage(uint256 swapFeePercentage) external;

    function setAssetManagerPoolConfig(IERC20 token, bytes memory poolConfig) external;
}

// File: @balancer-labs/v2-solidity-utils/contracts/helpers/WordCodec.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 "@balancer-labs/v2-interfaces/contracts/solidity-utils/helpers/BalancerErrors.sol";

import "../math/Math.sol";

/**
 * @dev Library for encoding and decoding values stored inside a 256 bit word. Typically used to pack multiple values in
 * a single storage slot, saving gas by performing less storage accesses.
 *
 * Each value is defined by its size and the least significant bit in the word, also known as offset. For example, two
 * 128 bit values may be encoded in a word by assigning one an offset of 0, and the other an offset of 128.
 *
 * We could use Solidity structs to pack values together in a single storage slot instead of relying on a custom and
 * error-prone library, but unfortunately Solidity only allows for structs to live in either storage, calldata or
 * memory. Because a memory struct uses not just memory but also a slot in the stack (to store its memory location),
 * using memory for word-sized values (i.e. of 256 bits or less) is strictly less gas performant, and doesn't even
 * prevent stack-too-deep issues. This is compounded by the fact that Balancer contracts typically are memory-intensive,
 * and the cost of accesing memory increases quadratically with the number of allocated words. Manual packing and
 * unpacking is therefore the preferred approach.
 */
library WordCodec {
    // Masks are values with the least significant N bits set. They can be used to extract an encoded value from a word,
    // or to insert a new one replacing the old.
    uint256 private constant _MASK_1 = 2**(1) - 1;
    uint256 private constant _MASK_192 = 2**(192) - 1;

    // In-place insertion

    /**
     * @dev Inserts an unsigned integer of bitLength, shifted by an offset, into a 256 bit word,
     * replacing the old value. Returns the new word.
     */
    function insertUint(
        bytes32 word,
        uint256 value,
        uint256 offset,
        uint256 bitLength
    ) internal pure returns (bytes32) {
        _validateEncodingParams(value, offset, bitLength);

        uint256 mask = (1 << bitLength) - 1;
        bytes32 clearedWord = bytes32(uint256(word) & ~(mask << offset));
        return clearedWord | bytes32(value << offset);
    }

    /**
     * @dev Inserts a signed integer shifted by an offset into a 256 bit word, replacing the old value. Returns
     * the new word.
     *
     * Assumes `value` can be represented using `bitLength` bits.
     */
    function insertInt(
        bytes32 word,
        int256 value,
        uint256 offset,
        uint256 bitLength
    ) internal pure returns (bytes32) {
        _validateEncodingParams(value, offset, bitLength);

        uint256 mask = (1 << bitLength) - 1;
        bytes32 clearedWord = bytes32(uint256(word) & ~(mask << offset));
        // Integer values need masking to remove the upper bits of negative values.
        return clearedWord | bytes32((uint256(value) & mask) << offset);
    }

    // Encoding

    /**
     * @dev Encodes an unsigned integer shifted by an offset. Ensures value fits within
     * `bitLength` bits.
     *
     * The return value can be ORed bitwise with other encoded values to form a 256 bit word.
     */
    function encodeUint(
        uint256 value,
        uint256 offset,
        uint256 bitLength
    ) internal pure returns (bytes32) {
        _validateEncodingParams(value, offset, bitLength);

        return bytes32(value << offset);
    }

    /**
     * @dev Encodes a signed integer shifted by an offset.
     *
     * The return value can be ORed bitwise with other encoded values to form a 256 bit word.
     */
    function encodeInt(
        int256 value,
        uint256 offset,
        uint256 bitLength
    ) internal pure returns (bytes32) {
        _validateEncodingParams(value, offset, bitLength);

        uint256 mask = (1 << bitLength) - 1;
        // Integer values need masking to remove the upper bits of negative values.
        return bytes32((uint256(value) & mask) << offset);
    }

    // Decoding

    /**
     * @dev Decodes and returns an unsigned integer with `bitLength` bits, shifted by an offset, from a 256 bit word.
     */
    function decodeUint(
        bytes32 word,
        uint256 offset,
        uint256 bitLength
    ) internal pure returns (uint256) {
        return uint256(word >> offset) & ((1 << bitLength) - 1);
    }

    /**
     * @dev Decodes and returns a signed integer with `bitLength` bits, shifted by an offset, from a 256 bit word.
     */
    function decodeInt(
        bytes32 word,
        uint256 offset,
        uint256 bitLength
    ) internal pure returns (int256) {
        int256 maxInt = int256((1 << (bitLength - 1)) - 1);
        uint256 mask = (1 << bitLength) - 1;

        int256 value = int256(uint256(word >> offset) & mask);
        // In case the decoded value is greater than the max positive integer that can be represented with bitLength
        // bits, we know it was originally a negative integer. Therefore, we mask it to restore the sign in the 256 bit
        // representation.
        return value > maxInt ? (value | int256(~mask)) : value;
    }

    // Special cases

    /**
     * @dev Decodes and returns a boolean shifted by an offset from a 256 bit word.
     */
    function decodeBool(bytes32 word, uint256 offset) internal pure returns (bool) {
        return (uint256(word >> offset) & _MASK_1) == 1;
    }

    /**
     * @dev Inserts a 192 bit value shifted by an offset into a 256 bit word, replacing the old value.
     * Returns the new word.
     *
     * Assumes `value` can be represented using 192 bits.
     */
    function insertBits192(
        bytes32 word,
        bytes32 value,
        uint256 offset
    ) internal pure returns (bytes32) {
        bytes32 clearedWord = bytes32(uint256(word) & ~(_MASK_192 << offset));
        return clearedWord | bytes32((uint256(value) & _MASK_192) << offset);
    }

    /**
     * @dev Inserts a boolean value shifted by an offset into a 256 bit word, replacing the old value. Returns the new
     * word.
     */
    function insertBool(
        bytes32 word,
        bool value,
        uint256 offset
    ) internal pure returns (bytes32) {
        bytes32 clearedWord = bytes32(uint256(word) & ~(_MASK_1 << offset));
        return clearedWord | bytes32(uint256(value ? 1 : 0) << offset);
    }

    // Helpers

    function _validateEncodingParams(
        uint256 value,
        uint256 offset,
        uint256 bitLength
    ) private pure {
        _require(offset < 256, Errors.OUT_OF_BOUNDS);
        // We never accept 256 bit values (which would make the codec pointless), and the larger the offset the smaller
        // the maximum bit length.
        _require(bitLength >= 1 && bitLength <= Math.min(255, 256 - offset), Errors.OUT_OF_BOUNDS);

        // Testing unsigned values for size is straightforward: their upper bits must be cleared.
        _require(value >> bitLength == 0, Errors.CODEC_OVERFLOW);
    }

    function _validateEncodingParams(
        int256 value,
        uint256 offset,
        uint256 bitLength
    ) private pure {
        _require(offset < 256, Errors.OUT_OF_BOUNDS);
        // We never accept 256 bit values (which would make the codec pointless), and the larger the offset the smaller
        // the maximum bit length.
        _require(bitLength >= 1 && bitLength <= Math.min(255, 256 - offset), Errors.OUT_OF_BOUNDS);

        // Testing signed values for size is a bit more involved.
        if (value >= 0) {
            // For positive values, we can simply check that the upper bits are clear. Notice we remove one bit from the
            // length for the sign bit.
            _require(value >> (bitLength - 1) == 0, Errors.CODEC_OVERFLOW);
        } else {
            // Negative values can receive the same treatment by making them positive, with the caveat that the range
            // for negative values in two's complement supports one more value than for the positive case.
            _require(Math.abs(value + 1) >> (bitLength - 1) == 0, Errors.CODEC_OVERFLOW);
        }
    }
}

// File: @balancer-labs/v2-solidity-utils/contracts/helpers/TemporarilyPausable.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 "@balancer-labs/v2-interfaces/contracts/solidity-utils/helpers/BalancerErrors.sol";
import "@balancer-labs/v2-interfaces/contracts/solidity-utils/helpers/ITemporarilyPausable.sol";

/**
 * @dev Allows for a contract to be paused during an initial period after deployment, disabling functionality. Can be
 * used as an emergency switch in case a security vulnerability or threat is identified.
 *
 * The contract can only be paused during the Pause Window, a period that starts at deployment. It can also be
 * unpaused and repaused any number of times during this period. This is intended to serve as a safety measure: it lets
 * system managers react quickly to potentially dangerous situations, knowing that this action is reversible if careful
 * analysis later determines there was a false alarm.
 *
 * If the contract is paused when the Pause Window finishes, it will remain in the paused state through an additional
 * Buffer Period, after which it will be automatically unpaused forever. This is to ensure there is always enough time
 * to react to an emergency, even if the threat is discovered shortly before the Pause Window expires.
 *
 * Note that since the contract can only be paused within the Pause Window, unpausing during the Buffer Period is
 * irreversible.
 */
abstract contract TemporarilyPausable is ITemporarilyPausable {
    // The Pause Window and Buffer Period are timestamp-based: they should not be relied upon for sub-minute accuracy.
    // solhint-disable not-rely-on-time

    uint256 private constant _MAX_PAUSE_WINDOW_DURATION = 90 days;
    uint256 private constant _MAX_BUFFER_PERIOD_DURATION = 30 days;

    uint256 private immutable _pauseWindowEndTime;
    uint256 private immutable _bufferPeriodEndTime;

    bool private _paused;

    constructor(uint256 pauseWindowDuration, uint256 bufferPeriodDuration) {
        _require(pauseWindowDuration <= _MAX_PAUSE_WINDOW_DURATION, Errors.MAX_PAUSE_WINDOW_DURATION);
        _require(bufferPeriodDuration <= _MAX_BUFFER_PERIOD_DURATION, Errors.MAX_BUFFER_PERIOD_DURATION);

        uint256 pauseWindowEndTime = block.timestamp + pauseWindowDuration;

        _pauseWindowEndTime = pauseWindowEndTime;
        _bufferPeriodEndTime = pauseWindowEndTime + bufferPeriodDuration;
    }

    /**
     * @dev Reverts if the contract is paused.
     */
    modifier whenNotPaused() {
        _ensureNotPaused();
        _;
    }

    /**
     * @dev Returns the current contract pause status, as well as the end times of the Pause Window and Buffer
     * Period.
     */
    function getPausedState()
        external
        view
        override
        returns (
            bool paused,
            uint256 pauseWindowEndTime,
            uint256 bufferPeriodEndTime
        )
    {
        paused = !_isNotPaused();
        pauseWindowEndTime = _getPauseWindowEndTime();
        bufferPeriodEndTime = _getBufferPeriodEndTime();
    }

    /**
     * @dev Sets the pause state to `paused`. The contract can only be paused until the end of the Pause Window, and
     * unpaused until the end of the Buffer Period.
     *
     * Once the Buffer Period expires, this function reverts unconditionally.
     */
    function _setPaused(bool paused) internal {
        if (paused) {
            _require(block.timestamp < _getPauseWindowEndTime(), Errors.PAUSE_WINDOW_EXPIRED);
        } else {
            _require(block.timestamp < _getBufferPeriodEndTime(), Errors.BUFFER_PERIOD_EXPIRED);
        }

        _paused = paused;
        emit PausedStateChanged(paused);
    }

    /**
     * @dev Reverts if the contract is paused.
     */
    function _ensureNotPaused() internal view {
        _require(_isNotPaused(), Errors.PAUSED);
    }

    /**
     * @dev Reverts if the contract is not paused.
     */
    function _ensurePaused() internal view {
        _require(!_isNotPaused(), Errors.NOT_PAUSED);
    }

    /**
     * @dev Returns true if the contract is unpaused.
     *
     * Once the Buffer Period expires, the gas cost of calling this function is reduced dramatically, as storage is no
     * longer accessed.
     */
    function _isNotPaused() internal view returns (bool) {
        // After the Buffer Period, the (inexpensive) timestamp check short-circuits the storage access.
        return block.timestamp > _getBufferPeriodEndTime() || !_paused;
    }

    // These getters lead to reduced bytecode size by inlining the immutable variables in a single place.

    function _getPauseWindowEndTime() private view returns (uint256) {
        return _pauseWindowEndTime;
    }

    function _getBufferPeriodEndTime() private view returns (uint256) {
        return _bufferPeriodEndTime;
    }
}

// File: @balancer-labs/v2-solidity-utils/contracts/openzeppelin/ERC20.sol



// SPDX-License-Identifier: MIT

pragma solidity ^0.7.0;

import "@balancer-labs/v2-interfaces/contracts/solidity-utils/helpers/BalancerErrors.sol";
import "@balancer-labs/v2-interfaces/contracts/solidity-utils/openzeppelin/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}. The total supply should only be read using this function
     *
     * Can be overridden by derived contracts to store the total supply in a different way (e.g. packed with other
     * storage values).
     */
    function totalSupply() public view virtual override returns (uint256) {
        return _totalSupply;
    }

    /**
     * @dev Sets a new value for the total supply. It should only be set using this function.
     *
     * * Can be overridden by derived contracts to store the total supply in a different way (e.g. packed with other
     * storage values).
     */
    function _setTotalSupply(uint256 value) internal virtual {
        _totalSupply = value;
    }

    /**
     * @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 {
        _beforeTokenTransfer(address(0), account, amount);

        _setTotalSupply(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_BALANCE);
        _setTotalSupply(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 {
        _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 {
        // solhint-disable-previous-line no-empty-blocks
    }
}

// File: @balancer-labs/v2-pool-utils/contracts/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 "@balancer-labs/v2-interfaces/contracts/vault/IVault.sol";

import "@balancer-labs/v2-solidity-utils/contracts/openzeppelin/ERC20Permit.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`
 * - Assigns infinite allowance for all token holders to the Vault
 */
contract BalancerPoolToken is ERC20Permit {
    IVault private immutable _vault;

    constructor(
        string memory tokenName,
        string memory tokenSymbol,
        IVault vault
    ) ERC20(tokenName, tokenSymbol) ERC20Permit(tokenName) {
        _vault = vault;
    }

    function getVault() public view returns (IVault) {
        return _vault;
    }

    // Overrides

    /**
     * @dev Override to grant the Vault infinite allowance, causing for Pool Tokens to not require approval.
     *
     * This is sound as the Vault already provides authorization mechanisms when initiation token transfers, which this
     * contract inherits.
     */
    function allowance(address owner, address spender) public view override returns (uint256) {
        if (spender == address(getVault())) {
            return uint256(-1);
        } else {
            return super.allowance(owner, spender);
        }
    }

    /**
     * @dev Override to allow for 'infinite allowance' and let the token owner use `transferFrom` with no self-allowance
     */
    function transferFrom(
        address sender,
        address recipient,
        uint256 amount
    ) public override returns (bool) {
        uint256 currentAllowance = allowance(sender, msg.sender);
        _require(msg.sender == sender || currentAllowance >= amount, Errors.ERC20_TRANSFER_EXCEEDS_ALLOWANCE);

        _transfer(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
            _approve(sender, msg.sender, currentAllowance - amount);
        }

        return true;
    }

    /**
     * @dev Override to allow decreasing allowance by more than the current amount (setting it to zero)
     */
    function decreaseAllowance(address spender, uint256 amount) public override returns (bool) {
        uint256 currentAllowance = allowance(msg.sender, spender);

        if (amount >= currentAllowance) {
            _approve(msg.sender, spender, 0);
        } else {
            // No risk of underflow due to if condition
            _approve(msg.sender, spender, currentAllowance - amount);
        }

        return true;
    }

    // Internal functions

    function _mintPoolTokens(address recipient, uint256 amount) internal {
        _mint(recipient, amount);
    }

    function _burnPoolTokens(address sender, uint256 amount) internal {
        _burn(sender, amount);
    }
}

// File: @balancer-labs/v2-pool-utils/contracts/BasePoolAuthorization.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 "@balancer-labs/v2-interfaces/contracts/vault/IAuthorizer.sol";

import "@balancer-labs/v2-solidity-utils/contracts/helpers/Authentication.sol";

/**
 * @dev Base authorization layer implementation for Pools.
 *
 * The owner account can call some of the permissioned functions - access control of the rest is delegated to the
 * Authorizer. Note that this owner is immutable: more sophisticated permission schemes, such as multiple ownership,
 * granular roles, etc., could be built on top of this by making the owner a smart contract.
 *
 * Access control of all other permissioned functions is delegated to an Authorizer. It is also possible to delegate
 * control of *all* permissioned functions to the Authorizer by setting the owner address to `_DELEGATE_OWNER`.
 */
abstract contract BasePoolAuthorization is Authentication {
    address private immutable _owner;

    address private constant _DELEGATE_OWNER = 0xBA1BA1ba1BA1bA1bA1Ba1BA1ba1BA1bA1ba1ba1B;

    constructor(address owner) {
        _owner = owner;
    }

    function getOwner() public view returns (address) {
        return _owner;
    }

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

    function _canPerform(bytes32 actionId, address account) internal view override returns (bool) {
        if ((getOwner() != _DELEGATE_OWNER) && _isOwnerOnlyAction(actionId)) {
            // Only the owner can perform "owner only" actions, unless the owner is delegated.
            return msg.sender == getOwner();
        } else {
            // Non-owner actions are always processed via the Authorizer, as "owner only" ones are when delegated.
            return _getAuthorizer().canPerform(actionId, account, address(this));
        }
    }

    function _isOwnerOnlyAction(bytes32) internal view virtual returns (bool) {
        return false;
    }

    function _getAuthorizer() internal view virtual returns (IAuthorizer);
}

// File: @balancer-labs/v2-pool-utils/contracts/RecoveryMode.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 "@balancer-labs/v2-interfaces/contracts/solidity-utils/helpers/BalancerErrors.sol";
import "@balancer-labs/v2-interfaces/contracts/pool-utils/BasePoolUserData.sol";
import "@balancer-labs/v2-interfaces/contracts/pool-utils/IRecoveryMode.sol";

import "@balancer-labs/v2-solidity-utils/contracts/math/FixedPoint.sol";

import "./BasePoolAuthorization.sol";

/**
 * @notice Handle storage and state changes for pools that support "Recovery Mode".
 *
 * @dev This is intended to provide a safe way to exit any pool during some kind of emergency, to avoid locking funds
 * in the event the pool enters a non-functional state (i.e., some code that normally runs during exits is causing
 * them to revert).
 *
 * Recovery Mode is *not* the same as pausing the pool. The pause function is only available during a short window
 * after factory deployment. Pausing can only be intentionally reversed during a buffer period, and the contract
 * will permanently unpause itself thereafter. Paused pools are completely disabled, in a kind of suspended animation,
 * until they are voluntarily or involuntarily unpaused.
 *
 * By contrast, a privileged account - typically a governance multisig - can place a pool in Recovery Mode at any
 * time, and it is always reversible. The pool is *not* disabled while in this mode: though of course whatever
 * condition prompted the transition to Recovery Mode has likely effectively disabled some functions. Rather,
 * a special "clean" exit is enabled, which runs the absolute minimum code necessary to exit proportionally.
 * In particular, stable pools do not attempt to compute the invariant (which is a complex, iterative calculation
 * that can fail in extreme circumstances), and no protocol fees are collected.
 *
 * It is critical to ensure that turning on Recovery Mode would do no harm, if activated maliciously or in error.
 */
abstract contract RecoveryMode is IRecoveryMode, BasePoolAuthorization {
    using FixedPoint for uint256;
    using BasePoolUserData for bytes;

    /**
     * @dev Reverts if the contract is in Recovery Mode.
     */
    modifier whenNotInRecoveryMode() {
        _ensureNotInRecoveryMode();
        _;
    }

    /**
     * @notice Enable recovery mode, which enables a special safe exit path for LPs.
     * @dev Does not otherwise affect pool operations (beyond deferring payment of protocol fees), though some pools may
     * perform certain operations in a "safer" manner that is less likely to fail, in an attempt to keep the pool
     * running, even in a pathological state. Unlike the Pause operation, which is only available during a short window
     * after factory deployment, Recovery Mode can always be enabled.
     */
    function enableRecoveryMode() external override authenticate {
        _setRecoveryMode(true);
    }

    /**
     * @notice Disable recovery mode, which disables the special safe exit path for LPs.
     * @dev Protocol fees are not paid while in Recovery Mode, so it should only remain active for as long as strictly
     * necessary.
     *
     * This function will revert when called within a Vault context (i.e. in the middle of a join or an exit).
     *
     * This function depends on the invariant value, which may be calculated incorrectly in the middle of a join or
     * an exit, because the state of the pool could be out of sync with the state of the Vault.
     * `_onDisableRecoveryMode` will revert when called from such a context for composable stable pools, effectively
     * protecting this function.
     *
     * See https://forum.balancer.fi/t/reentrancy-vulnerability-scope-expanded/4345 for reference.
     */
    function disableRecoveryMode() external override authenticate {
        _setRecoveryMode(false);
    }

    // Defer implementation for functions that require storage

    /**
     * @notice Override to check storage and return whether the pool is in Recovery Mode
     */
    function inRecoveryMode() public view virtual override returns (bool);

    /**
     * @dev Override to update storage and emit the event
     *
     * No complex code or external calls that could fail should be placed in the implementations,
     * which could jeopardize the ability to enable and disable Recovery Mode.
     */
    function _setRecoveryMode(bool enabled) internal virtual;

    /**
     * @dev Reverts if the contract is not in Recovery Mode.
     */
    function _ensureInRecoveryMode() internal view {
        _require(inRecoveryMode(), Errors.NOT_IN_RECOVERY_MODE);
    }

    /**
     * @dev Reverts if the contract is in Recovery Mode.
     */
    function _ensureNotInRecoveryMode() internal view {
        _require(!inRecoveryMode(), Errors.IN_RECOVERY_MODE);
    }

    /**
     * @dev A minimal proportional exit, suitable as is for most pools: though not for pools with preminted BPT
     * or other special considerations. Designed to be overridden if a pool needs to do extra processing,
     * such as scaling a stored invariant, or caching the new total supply.
     *
     * No complex code or external calls should be made in derived contracts that override this!
     */
    function _doRecoveryModeExit(
        uint256[] memory balances,
        uint256 totalSupply,
        bytes memory userData
    ) internal virtual returns (uint256, uint256[] memory) {
        uint256 bptAmountIn = userData.recoveryModeExit();

        uint256[] memory amountsOut = _computeProportionalAmountsOut(balances, totalSupply, bptAmountIn);

        return (bptAmountIn, amountsOut);
    }

    function _computeProportionalAmountsOut(
        uint256[] memory balances,
        uint256 totalSupply,
        uint256 bptAmountIn
    ) internal pure returns (uint256[] memory amountsOut) {
        /**********************************************************************************************
        // exactBPTInForTokensOut                                                                    //
        // (per token)                                                                               //
        // aO = tokenAmountOut             /        bptIn         \                                  //
        // b = tokenBalance      a0 = b * | ---------------------  |                                 //
        // bptIn = bptAmountIn             \     bptTotalSupply    /                                 //
        // bpt = bptTotalSupply                                                                      //
        **********************************************************************************************/

        // Since we're computing an amount out, we round down overall. This means rounding down on both the
        // multiplication and division.

        uint256 bptRatio = bptAmountIn.divDown(totalSupply);

        amountsOut = new uint256[](balances.length);
        for (uint256 i = 0; i < balances.length; i++) {
            amountsOut[i] = balances[i].mulDown(bptRatio);
        }
    }
}

// File: @balancer-labs/v2-solidity-utils/contracts/openzeppelin/SafeMath.sol



// SPDX-License-Identifier: MIT

pragma solidity ^0.7.0;

import "@balancer-labs/v2-interfaces/contracts/solidity-utils/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: @balancer-labs/v2-solidity-utils/contracts/openzeppelin/ERC20Permit.sol



// SPDX-License-Identifier: MIT

pragma solidity ^0.7.0;

import "@balancer-labs/v2-interfaces/contracts/solidity-utils/openzeppelin/IERC20Permit.sol";

import "./ERC20.sol";
import "../helpers/EOASignaturesValidator.sol";

/**
 * @dev Implementation of the ERC20 Permit extension allowing approvals to be made via signatures, as defined in
 * https://eips.ethereum.org/EIPS/eip-2612[EIP-2612].
 *
 * Adds the {permit} method, which can be used to change an account's ERC20 allowance (see {IERC20-allowance}) by
 * presenting a message signed by the account. By not relying on `{IERC20-approve}`, the token holder account doesn't
 * need to send a transaction, and thus is not required to hold Ether at all.
 *
 * _Available since v3.4._
 */
abstract contract ERC20Permit is ERC20, IERC20Permit, EOASignaturesValidator {
    // solhint-disable-next-line var-name-mixedcase
    bytes32 private constant _PERMIT_TYPEHASH = keccak256(
        "Permit(address owner,address spender,uint256 value,uint256 nonce,uint256 deadline)"
    );

    /**
     * @dev Initializes the {EIP712} domain separator using the `name` parameter, and setting `version` to `"1"`.
     *
     * It's a good idea to use the same `name` that is defined as the ERC20 token name.
     */
    constructor(string memory name) EIP712(name, "1") {
        // solhint-disable-previous-line no-empty-blocks
    }

    /**
     * @dev See {IERC20Permit-permit}.
     */
    function permit(
        address owner,
        address spender,
        uint256 value,
        uint256 deadline,
        uint8 v,
        bytes32 r,
        bytes32 s
    ) public virtual override {
        bytes32 structHash = keccak256(
            abi.encode(_PERMIT_TYPEHASH, owner, spender, value, getNextNonce(owner), deadline)
        );

        _ensureValidSignature(owner, structHash, _toArraySignature(v, r, s), deadline, Errors.INVALID_SIGNATURE);

        _approve(owner, spender, value);
    }

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

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

// File: @balancer-labs/v2-interfaces/contracts/solidity-utils/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: @balancer-labs/v2-solidity-utils/contracts/helpers/EOASignaturesValidator.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 "@balancer-labs/v2-interfaces/contracts/solidity-utils/helpers/BalancerErrors.sol";
import "@balancer-labs/v2-interfaces/contracts/solidity-utils/helpers/ISignaturesValidator.sol";

import "../openzeppelin/EIP712.sol";

/**
 * @dev Utility for signing Solidity function calls.
 */
abstract contract EOASignaturesValidator is ISignaturesValidator, EIP712 {
    // Replay attack prevention for each account.
    mapping(address => uint256) internal _nextNonce;

    function getDomainSeparator() public view override returns (bytes32) {
        return _domainSeparatorV4();
    }

    function getNextNonce(address account) public view override returns (uint256) {
        return _nextNonce[account];
    }

    function _ensureValidSignature(
        address account,
        bytes32 structHash,
        bytes memory signature,
        uint256 errorCode
    ) internal {
        return _ensureValidSignature(account, structHash, signature, type(uint256).max, errorCode);
    }

    function _ensureValidSignature(
        address account,
        bytes32 structHash,
        bytes memory signature,
        uint256 deadline,
        uint256 errorCode
    ) internal {
        bytes32 digest = _hashTypedDataV4(structHash);
        _require(_isValidSignature(account, digest, signature), errorCode);

        // We could check for the deadline before validating the signature, but this leads to saner error processing (as
        // we only care about expired deadlines if the signature is correct) and only affects the gas cost of the revert
        // scenario, which will only occur infrequently, if ever.
        // The deadline is timestamp-based: it should not be relied upon for sub-minute accuracy.
        // solhint-disable-next-line not-rely-on-time
        _require(deadline >= block.timestamp, Errors.EXPIRED_SIGNATURE);

        // We only advance the nonce after validating the signature. This is irrelevant for this module, but it can be
        // important in derived contracts that override _isValidSignature (e.g. SignaturesValidator), as we want for
        // the observable state to still have the current nonce as the next valid one.
        _nextNonce[account] += 1;
    }

    function _isValidSignature(
        address account,
        bytes32 digest,
        bytes memory signature
    ) internal view virtual returns (bool) {
        _require(signature.length == 65, Errors.MALFORMED_SIGNATURE);

        bytes32 r;
        bytes32 s;
        uint8 v;

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

        address recoveredAddress = ecrecover(digest, v, r, s);

        // ecrecover returns the zero address on recover failure, so we need to handle that explicitly.
        return (recoveredAddress != address(0) && recoveredAddress == account);
    }

    function _toArraySignature(
        uint8 v,
        bytes32 r,
        bytes32 s
    ) internal pure returns (bytes memory) {
        bytes memory signature = new bytes(65);
        // solhint-disable-next-line no-inline-assembly
        assembly {
            mstore(add(signature, 32), r)
            mstore(add(signature, 64), s)
            mstore8(add(signature, 96), v)
        }

        return signature;
    }
}

// File: @balancer-labs/v2-solidity-utils/contracts/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()
        }
    }
}

// File: @balancer-labs/v2-interfaces/contracts/pool-utils/BasePoolUserData.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;

library BasePoolUserData {
    // Special ExitKind for all pools, used in Recovery Mode. Use the max 8-bit value to prevent conflicts
    // with future additions to the ExitKind enums (or any front-end code that maps to existing values)
    uint8 public constant RECOVERY_MODE_EXIT_KIND = 255;

    // Return true if this is the special exit kind.
    function isRecoveryModeExitKind(bytes memory self) internal pure returns (bool) {
        // Check for the "no data" case, or abi.decode would revert
        return self.length > 0 && abi.decode(self, (uint8)) == RECOVERY_MODE_EXIT_KIND;
    }

    // Parse the bptAmountIn out of the userData
    function recoveryModeExit(bytes memory self) internal pure returns (uint256 bptAmountIn) {
        (, bptAmountIn) = abi.decode(self, (uint8, uint256));
    }
}

// File: @balancer-labs/v2-interfaces/contracts/pool-utils/IRecoveryMode.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 RecoveryMode module.
 */
interface IRecoveryMode {
    /**
     * @dev Emitted when the Recovery Mode status changes.
     */
    event RecoveryModeStateChanged(bool enabled);

    /**
     * @notice Enables Recovery Mode in the Pool, disabling protocol fee collection and allowing for safe proportional
     * exits with low computational complexity and no dependencies.
     */
    function enableRecoveryMode() external;

    /**
     * @notice Disables Recovery Mode in the Pool, restoring protocol fee collection and disallowing proportional exits.
     */
    function disableRecoveryMode() external;

    /**
     * @notice Returns true if the Pool is in Recovery Mode.
     */
    function inRecoveryMode() external view returns (bool);
}

// File: @balancer-labs/v2-pool-utils/contracts/protocol-fees/ProtocolFeeCache.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 "@balancer-labs/v2-interfaces/contracts/solidity-utils/helpers/BalancerErrors.sol";
import "@balancer-labs/v2-interfaces/contracts/standalone-utils/IProtocolFeePercentagesProvider.sol";

import "@balancer-labs/v2-solidity-utils/contracts/openzeppelin/SafeCast.sol";

import "../RecoveryMode.sol";

/**
 * @dev The Vault does not provide the protocol swap fee percentage in swap hooks (as swaps don't typically need this
 * value), so for swaps that need this value, we would have to to fetch it ourselves from the
 * ProtocolFeePercentagesProvider. Additionally, other protocol fee types (such as Yield or AUM) can only be obtained
 * by making said call.
 *
 * However, these values change so rarely that it doesn't make sense to perform the required calls to get the current
 * values in every single user interaction. Instead, we keep a local copy that can be permissionlessly updated by anyone
 * with the real value. We also pack these values together, performing a single storage read to get them all.
 *
 * When initialized with a special sentinel value, the swap fee is delegated, meaning the mutable protocol swap fee
 * cache is set to the current value stored in the ProtocolFeePercentagesProvider, and can be updated by anyone with a
 * call to `updateProtocolFeePercentageCache`. Any other value means the protocol swap fee is fixed, so it is instead
 * stored in the immutable `_fixedProtocolSwapFeePercentage`.
 */
abstract contract ProtocolFeeCache is RecoveryMode {
    using SafeCast for uint256;

    IProtocolFeePercentagesProvider private immutable _protocolFeeProvider;

    // Protocol Fee Percentages can never be larger than 100% (1e18), which fits in ~59 bits, so using 64 for each type
    // is sufficient.
    struct FeeTypeCache {
        uint64 swapFee;
        uint64 yieldFee;
        uint64 aumFee;
    }

    FeeTypeCache private _cache;

    event ProtocolFeePercentageCacheUpdated(uint256 indexed feeType, uint256 protocolFeePercentage);

    // Swap fees can be set to a fixed value at construction, or delegated to the ProtocolFeePercentagesProvider if
    // passing the special sentinel value.
    uint256 public constant DELEGATE_PROTOCOL_SWAP_FEES_SENTINEL = type(uint256).max;

    bool private immutable _delegatedProtocolSwapFees;

    // Only valid when `_delegatedProtocolSwapFees` is false
    uint256 private immutable _fixedProtocolSwapFeePercentage;

    constructor(IProtocolFeePercentagesProvider protocolFeeProvider, uint256 protocolSwapFeePercentage) {
        // Protocol swap fees are delegated to the value reported by the ProtocolFeePercentagesProvider if the sentinel
        // value is passed.
        bool delegatedProtocolSwapFees = protocolSwapFeePercentage == DELEGATE_PROTOCOL_SWAP_FEES_SENTINEL;

        _delegatedProtocolSwapFees = delegatedProtocolSwapFees;
        _protocolFeeProvider = protocolFeeProvider;

        _updateProtocolFeeCache(protocolFeeProvider, ProtocolFeeType.YIELD);
        _updateProtocolFeeCache(protocolFeeProvider, ProtocolFeeType.AUM);

        if (delegatedProtocolSwapFees) {
            _updateProtocolFeeCache(protocolFeeProvider, ProtocolFeeType.SWAP);
        } else {
            _require(
                protocolSwapFeePercentage <= protocolFeeProvider.getFeeTypeMaximumPercentage(ProtocolFeeType.SWAP),
                Errors.SWAP_FEE_PERCENTAGE_TOO_HIGH
            );

            // We cannot set `_fixedProtocolSwapFeePercentage` here due to it being immutable so instead we must set it
            // in the main function scope with a value based on whether protocol fees are delegated.

            // Emit an event as we do in `_updateProtocolFeeCache` to appear the same to offchain indexers.
            emit ProtocolFeePercentageCacheUpdated(ProtocolFeeType.SWAP, protocolSwapFeePercentage);
        }

        // As `_fixedProtocolSwapFeePercentage` is immutable we must set a value, but just set to zero if it's not used.
        _fixedProtocolSwapFeePercentage = delegatedProtocolSwapFees ? 0 : protocolSwapFeePercentage;
    }

    /**
     * @dev Returns the cached protocol fee percentage. If `getProtocolSwapFeeDelegation()` is false, this value is
     * immutable for swap fee queries. Alternatively, it will track the global fee percentage set in the
     * ProtocolFeePercentagesProvider.
     */
    function getProtocolFeePercentageCache(uint256 feeType) public view returns (uint256) {
        if (inRecoveryMode()) {
            return 0;
        }

        if (feeType == ProtocolFeeType.SWAP) {
            return getProtocolSwapFeeDelegation() ? _cache.swapFee : _fixedProtocolSwapFeePercentage;
        } else if (feeType == ProtocolFeeType.YIELD) {
            return _cache.yieldFee;
        } else if (feeType == ProtocolFeeType.AUM) {
            return _cache.aumFee;
        } else {
            _revert(Errors.UNHANDLED_FEE_TYPE);
        }
    }

    /**
     * @dev Can be called by anyone to update the cached fee percentages (swap fee is only updated when delegated).
     * Updates the cache to the latest value set by governance.
     *
     * This function will revert when called within a Vault context (i.e. in the middle of a join or an exit).
     *
     * This function depends on the invariant value, which may be calculated incorrectly in the middle of a join or
     * an exit, because the state of the pool could be out of sync with the state of the Vault.
     * `_beforeProtocolFeeCacheUpdate` will revert when called from such a context for composable stable pools,
     * effectively protecting this function.
     *
     * See https://forum.balancer.fi/t/reentrancy-vulnerability-scope-expanded/4345 for reference.
     */
    function updateProtocolFeePercentageCache() external {
        _beforeProtocolFeeCacheUpdate();

        if (getProtocolSwapFeeDelegation()) {
            _updateProtocolFeeCache(_protocolFeeProvider, ProtocolFeeType.SWAP);
        }

        _updateProtocolFeeCache(_protocolFeeProvider, ProtocolFeeType.YIELD);
        _updateProtocolFeeCache(_protocolFeeProvider, ProtocolFeeType.AUM);
    }

    /**
     * @dev Override in derived contracts to perform some action before the cache is updated. This is typically relevant
     * to Pools that incur protocol debt between operations. To avoid altering the amount due retroactively, this debt
     * needs to be paid before the fee percentages change.
     */
    function _beforeProtocolFeeCacheUpdate() internal virtual {}

    /**
     * @dev Returns whether this Pool tracks protocol swap fee changes in the IProtocolFeePercentagesProvider.
     */
    function getProtocolSwapFeeDelegation() public view returns (bool) {
        return _delegatedProtocolSwapFees;
    }

    function _updateProtocolFeeCache(IProtocolFeePercentagesProvider protocolFeeProvider, uint256 feeType) private {
        uint256 currentValue = protocolFeeProvider.getFeeTypePercentage(feeType);

        if (feeType == ProtocolFeeType.SWAP) {
            _cache.swapFee = currentValue.toUint64();
        } else if (feeType == ProtocolFeeType.YIELD) {
            _cache.yieldFee = currentValue.toUint64();
        } else if (feeType == ProtocolFeeType.AUM) {
            _cache.aumFee = currentValue.toUint64();
        } else {
            _revert(Errors.UNHANDLED_FEE_TYPE);
        }

        emit ProtocolFeePercentageCacheUpdated(feeType, currentValue);
    }
}

// File: @balancer-labs/v2-pool-utils/contracts/protocol-fees/InvariantGrowthProtocolSwapFees.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 "@balancer-labs/v2-solidity-utils/contracts/math/FixedPoint.sol";
import "@balancer-labs/v2-solidity-utils/contracts/math/Math.sol";
import "./ProtocolFees.sol";

library InvariantGrowthProtocolSwapFees {
    using FixedPoint for uint256;

    function getProtocolOwnershipPercentage(
        uint256 invariantGrowthRatio,
        uint256 supplyGrowthRatio,
        uint256 protocolSwapFeePercentage
    ) internal pure returns (uint256) {
        // Joins and exits are symmetrical; for simplicity, we consider a join, where the invariant and supply
        // both increase.

        // |-------------------------|-- original invariant * invariantGrowthRatio
        // |   increase from fees    |
        // |-------------------------|-- original invariant * supply growth ratio (fee-less invariant)
        // |                         |
        // | increase from balances  |
        // |-------------------------|-- original invariant
        // |                         |
        // |                         |  |------------------|-- currentSupply
        // |                         |  |    BPT minted    |
        // |                         |  |------------------|-- previousSupply
        // |   original invariant    |  |  original supply |
        // |_________________________|  |__________________|
        //
        // If the join is proportional, the invariant and supply will likewise increase proportionally,
        // so the growth ratios (invariantGrowthRatio / supplyGrowthRatio) will be equal. In this case, we do not charge
        // any protocol fees.
        // We also charge no protocol fees in the case where `invariantGrowthRatio < supplyGrowthRatio` to avoid
        // potential underflows, however this should only occur in extremely low volume actions due solely to rounding
        // error.

        if ((supplyGrowthRatio >= invariantGrowthRatio) || (protocolSwapFeePercentage == 0)) return 0;

        // If the join is non-proportional, the supply increase will be proportionally less than the invariant increase,
        // since the BPT minted will be based on fewer tokens (because swap fees are not included). So the supply growth
        // is due entirely to the balance changes, while the invariant growth also includes swap fees.
        //
        // To isolate the amount of increase by fees then, we multiply the original invariant by the supply growth
        // ratio to get the "feeless invariant". The difference between the final invariant and this value is then
        // the amount of the invariant due to fees, which we convert to a percentage by normalizing against the
        // final invariant. This is expressed as the expression below:
        //
        // invariantGrowthFromFees = currentInvariant - supplyGrowthRatio * previousInvariant
        //
        // We then divide through by current invariant so the LHS can be identified as the fraction of the pool which
        // is made up of accumulated swap fees.
        //
        // swapFeesPercentage = 1 - supplyGrowthRatio * previousInvariant / currentInvariant
        //
        // We then define `invariantGrowthRatio` in a similar fashion to `supplyGrowthRatio` to give the result:
        //
        // swapFeesPercentage = 1 - supplyGrowthRatio / invariantGrowthRatio
        //
        // Using this form allows us to consider only the ratios of the two invariants, rather than their absolute
        // values: a useful property, as this is sometimes easier than calculating the full invariant twice.

        // We've already checked that `supplyGrowthRatio` is smaller than `invariantGrowthRatio`, and hence their ratio
        // smaller than FixedPoint.ONE, allowing for unchecked arithmetic.
        uint256 swapFeesPercentage = FixedPoint.ONE - supplyGrowthRatio.divDown(invariantGrowthRatio);

        // We then multiply by the protocol swap fee percentage to get the fraction of the pool which the protocol
        // should own once fees have been collected.
        return swapFeesPercentage.mulDown(protocolSwapFeePercentage);
    }

    function calcDueProtocolFees(
        uint256 invariantGrowthRatio,
        uint256 previousSupply,
        uint256 currentSupply,
        uint256 protocolSwapFeePercentage
    ) internal pure returns (uint256) {
        uint256 protocolOwnershipPercentage = getProtocolOwnershipPercentage(
            invariantGrowthRatio,
            currentSupply.divDown(previousSupply),
            protocolSwapFeePercentage
        );

        return ProtocolFees.bptForPoolOwnershipPercentage(currentSupply, protocolOwnershipPercentage);
    }
}

// File: @balancer-labs/v2-solidity-utils/contracts/openzeppelin/SafeCast.sol



// SPDX-License-Identifier: MIT

pragma solidity ^0.7.0;

import "@balancer-labs/v2-interfaces/contracts/solidity-utils/helpers/BalancerErrors.sol";

/**
 * @dev Wrappers over Solidity's uintXX/intXX casting operators with added overflow
 * checks.
 *
 * Downcasting from uint256/int256 in Solidity does not revert on overflow. This can
 * easily result in undesired exploitation or bugs, since developers usually
 * assume that overflows raise errors. `SafeCast` restores this intuition by
 * reverting the transaction when such 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.
 *
 * Can be combined with {SafeMath} and {SignedSafeMath} to extend it to smaller types, by performing
 * all math on `uint256` and `int256` and then downcasting.
 */
library SafeCast {
    /**
     * @dev Converts an unsigned uint256 into a signed int256.
     *
     * Requirements:
     *
     * - input must be less than or equal to maxInt256.
     */
    function toInt256(uint256 value) internal pure returns (int256) {
        _require(value >> 255 == 0, Errors.SAFE_CAST_VALUE_CANT_FIT_INT256);
        return int256(value);
    }

    /**
     * @dev Converts an unsigned uint256 into an unsigned uint64.
     *
     * Requirements:
     *
     * - input must be less than or equal to maxUint64.
     */
    function toUint64(uint256 value) internal pure returns (uint64) {
        _require(value <= type(uint64).max, Errors.SAFE_CAST_VALUE_CANT_FIT_UINT64);
        return uint64(value);
    }
}

// File: @balancer-labs/v2-pool-utils/contracts/protocol-fees/ProtocolFees.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 "@balancer-labs/v2-solidity-utils/contracts/math/FixedPoint.sol";
import "@balancer-labs/v2-solidity-utils/contracts/math/Math.sol";

library ProtocolFees {
    using FixedPoint for uint256;

    /**
     * @dev Calculates the amount of BPT necessary to give ownership of a given percentage of the Pool.
     * Note that this function reverts if `poolPercentage` >= 100%, it's expected that the caller will enforce this.
     * @param totalSupply - The total supply of the pool prior to minting BPT.
     * @param poolOwnershipPercentage - The desired ownership percentage of the pool to have as a result of minting BPT.
     * @return bptAmount - The amount of BPT to mint such that it is `poolPercentage` of the resultant total supply.
     */
    function bptForPoolOwnershipPercentage(uint256 totalSupply, uint256 poolOwnershipPercentage)
        internal
        pure
        returns (uint256)
    {
        // If we mint some amount `bptAmount` of BPT then the percentage ownership of the pool this grants is given by:
        // `poolOwnershipPercentage = bptAmount / (totalSupply + bptAmount)`.
        // Solving for `bptAmount`, we arrive at:
        // `bptAmount = totalSupply * poolOwnershipPercentage / (1 - poolOwnershipPercentage)`.
        return Math.divDown(Math.mul(totalSupply, poolOwnershipPercentage), poolOwnershipPercentage.complement());
    }
}