Make ERC4626 _deposit and _withdraw internal virtual (#3504)

// SPDX-License-Identifier: MIT

pragma solidity ^0.8.0;

import "../ERC20.sol";
import "../utils/SafeERC20.sol";
import "../../../interfaces/IERC4626.sol";
import "../../../utils/math/Math.sol";

/**
 * @dev Implementation of the ERC4626 "Tokenized Vault Standard" as defined in
 * https://eips.ethereum.org/EIPS/eip-4626[EIP-4626].
 *
 * This extension allows the minting and burning of "shares" (represented using the ERC20 inheritance) in exchange for
 * underlying "assets" through standardized {deposit}, {mint}, {redeem} and {burn} workflows. This contract extends
 * the ERC20 standard. Any additional extensions included along it would affect the "shares" token represented by this
 * contract and not the "assets" token which is an independent contract.
 *
 * CAUTION: Deposits and withdrawals may incur unexpected slippage. Users should verify that the amount received of
 * shares or assets is as expected. EOAs should operate through a wrapper that performs these checks such as
 * https://github.com/fei-protocol/ERC4626#erc4626router-and-base[ERC4626Router].
 *
 * _Available since v4.7._
 */
abstract contract ERC4626 is ERC20, IERC4626 {
    using Math for uint256;

    IERC20Metadata private immutable _asset;

    /**
     * @dev Set the underlying asset contract. This must be an ERC20-compatible contract (ERC20 or ERC777).
     */
    constructor(IERC20Metadata asset_) {
        _asset = asset_;
    }

    /** @dev See {IERC4262-asset} */
    function asset() public view virtual override returns (address) {
        return address(_asset);
    }

    /** @dev See {IERC4262-totalAssets} */
    function totalAssets() public view virtual override returns (uint256) {
        return _asset.balanceOf(address(this));
    }

    /** @dev See {IERC4262-convertToShares} */
    function convertToShares(uint256 assets) public view virtual override returns (uint256 shares) {
        return _convertToShares(assets, Math.Rounding.Down);
    }

    /** @dev See {IERC4262-convertToAssets} */
    function convertToAssets(uint256 shares) public view virtual override returns (uint256 assets) {
        return _convertToAssets(shares, Math.Rounding.Down);
    }

    /** @dev See {IERC4262-maxDeposit} */
    function maxDeposit(address) public view virtual override returns (uint256) {
        return _isVaultCollateralized() ? type(uint256).max : 0;
    }

    /** @dev See {IERC4262-maxMint} */
    function maxMint(address) public view virtual override returns (uint256) {
        return type(uint256).max;
    }

    /** @dev See {IERC4262-maxWithdraw} */
    function maxWithdraw(address owner) public view virtual override returns (uint256) {
        return _convertToAssets(balanceOf(owner), Math.Rounding.Down);
    }

    /** @dev See {IERC4262-maxRedeem} */
    function maxRedeem(address owner) public view virtual override returns (uint256) {
        return balanceOf(owner);
    }

    /** @dev See {IERC4262-previewDeposit} */
    function previewDeposit(uint256 assets) public view virtual override returns (uint256) {
        return _convertToShares(assets, Math.Rounding.Down);
    }

    /** @dev See {IERC4262-previewMint} */
    function previewMint(uint256 shares) public view virtual override returns (uint256) {
        return _convertToAssets(shares, Math.Rounding.Up);
    }

    /** @dev See {IERC4262-previewWithdraw} */
    function previewWithdraw(uint256 assets) public view virtual override returns (uint256) {
        return _convertToShares(assets, Math.Rounding.Up);
    }

    /** @dev See {IERC4262-previewRedeem} */
    function previewRedeem(uint256 shares) public view virtual override returns (uint256) {
        return _convertToAssets(shares, Math.Rounding.Down);
    }

    /** @dev See {IERC4262-deposit} */
    function deposit(uint256 assets, address receiver) public virtual override returns (uint256) {
        require(assets <= maxDeposit(receiver), "ERC4626: deposit more than max");

        uint256 shares = previewDeposit(assets);
        _deposit(_msgSender(), receiver, assets, shares);

        return shares;
    }

    /** @dev See {IERC4262-mint} */
    function mint(uint256 shares, address receiver) public virtual override returns (uint256) {
        require(shares <= maxMint(receiver), "ERC4626: mint more than max");

        uint256 assets = previewMint(shares);
        _deposit(_msgSender(), receiver, assets, shares);

        return assets;
    }

    /** @dev See {IERC4262-withdraw} */
    function withdraw(
        uint256 assets,
        address receiver,
        address owner
    ) public virtual override returns (uint256) {
        require(assets <= maxWithdraw(owner), "ERC4626: withdraw more than max");

        uint256 shares = previewWithdraw(assets);
        _withdraw(_msgSender(), receiver, owner, assets, shares);

        return shares;
    }

    /** @dev See {IERC4262-redeem} */
    function redeem(
        uint256 shares,
        address receiver,
        address owner
    ) public virtual override returns (uint256) {
        require(shares <= maxRedeem(owner), "ERC4626: redeem more than max");

        uint256 assets = previewRedeem(shares);
        _withdraw(_msgSender(), receiver, owner, assets, shares);

        return assets;
    }

    /**
     * @dev Internal convertion function (from assets to shares) with support for rounding direction
     *
     * Will revert if assets > 0, totalSupply > 0 and totalAssets = 0. That corresponds to a case where any asset
     * would represent an infinite amout of shares.
     */
    function _convertToShares(uint256 assets, Math.Rounding rounding) internal view virtual returns (uint256 shares) {
        uint256 supply = totalSupply();
        return
            (assets == 0 || supply == 0)
                ? assets.mulDiv(10**decimals(), 10**_asset.decimals(), rounding)
                : assets.mulDiv(supply, totalAssets(), rounding);
    }

    /**
     * @dev Internal convertion function (from shares to assets) with support for rounding direction
     */
    function _convertToAssets(uint256 shares, Math.Rounding rounding) internal view virtual returns (uint256 assets) {
        uint256 supply = totalSupply();
        return
            (supply == 0)
                ? shares.mulDiv(10**_asset.decimals(), 10**decimals(), rounding)
                : shares.mulDiv(totalAssets(), supply, rounding);
    }

    /**
     * @dev Deposit/mint common workflow
     */
    function _deposit(
        address caller,
        address receiver,
        uint256 assets,
        uint256 shares
    ) internal virtual {
        // If _asset is ERC777, `transferFrom` can trigger a reenterancy BEFORE the transfer happens through the
        // `tokensToSend` hook. On the other hand, the `tokenReceived` hook, that is triggered after the transfer,
        // calls the vault, which is assumed not malicious.
        //
        // Conclusion: we need to do the transfer before we mint so that any reentrancy would happen before the
        // assets are transfered and before the shares are minted, which is a valid state.
        // slither-disable-next-line reentrancy-no-eth
        SafeERC20.safeTransferFrom(_asset, caller, address(this), assets);
        _mint(receiver, shares);

        emit Deposit(caller, receiver, assets, shares);
    }

    /**
     * @dev Withdraw/redeem common workflow
     */
    function _withdraw(
        address caller,
        address receiver,
        address owner,
        uint256 assets,
        uint256 shares
    ) internal virtual {
        if (caller != owner) {
            _spendAllowance(owner, caller, shares);
        }

        // If _asset is ERC777, `transfer` can trigger trigger a reentrancy AFTER the transfer happens through the
        // `tokensReceived` hook. On the other hand, the `tokensToSend` hook, that is triggered before the transfer,
        // calls the vault, which is assumed not malicious.
        //
        // Conclusion: we need to do the transfer after the burn so that any reentrancy would happen after the
        // shares are burned and after the assets are transfered, which is a valid state.
        _burn(owner, shares);
        SafeERC20.safeTransfer(_asset, receiver, assets);

        emit Withdraw(caller, receiver, owner, assets, shares);
    }

    function _isVaultCollateralized() private view returns (bool) {
        return totalAssets() > 0 || totalSupply() == 0;
    }
}

// SPDX-License-Identifier: MIT

pragma solidity ^0.8.0;

import "../ERC20.sol";
import "../utils/SafeERC20.sol";
import "../../../interfaces/IERC4626.sol";
import "../../../utils/math/Math.sol";

/**
 * @dev Implementation of the ERC4626 "Tokenized Vault Standard" as defined in
 * https://eips.ethereum.org/EIPS/eip-4626[EIP-4626].
 *
 * This extension allows the minting and burning of "shares" (represented using the ERC20 inheritance) in exchange for
 * underlying "assets" through standardized {deposit}, {mint}, {redeem} and {burn} workflows. This contract extends
 * the ERC20 standard. Any additional extensions included along it would affect the "shares" token represented by this
 * contract and not the "assets" token which is an independent contract.
 *
 * CAUTION: Deposits and withdrawals may incur unexpected slippage. Users should verify that the amount received of
 * shares or assets is as expected. EOAs should operate through a wrapper that performs these checks such as
 * https://github.com/fei-protocol/ERC4626#erc4626router-and-base[ERC4626Router].
 *
 * _Available since v4.7._
 */
abstract contract ERC4626 is ERC20, IERC4626 {
    using Math for uint256;

    IERC20Metadata private immutable _asset;

    /**
     * @dev Set the underlying asset contract. This must be an ERC20-compatible contract (ERC20 or ERC777).
     */
    constructor(IERC20Metadata asset_) {
        _asset = asset_;
    }

    /** @dev See {IERC4262-asset} */
    function asset() public view virtual override returns (address) {
        return address(_asset);
    }

    /** @dev See {IERC4262-totalAssets} */
    function totalAssets() public view virtual override returns (uint256) {
        return _asset.balanceOf(address(this));
    }

    /** @dev See {IERC4262-convertToShares} */
    function convertToShares(uint256 assets) public view virtual override returns (uint256 shares) {
        return _convertToShares(assets, Math.Rounding.Down);
    }

    /** @dev See {IERC4262-convertToAssets} */
    function convertToAssets(uint256 shares) public view virtual override returns (uint256 assets) {
        return _convertToAssets(shares, Math.Rounding.Down);
    }

    /** @dev See {IERC4262-maxDeposit} */
    function maxDeposit(address) public view virtual override returns (uint256) {
        return _isVaultCollateralized() ? type(uint256).max : 0;
    }

    /** @dev See {IERC4262-maxMint} */
    function maxMint(address) public view virtual override returns (uint256) {
        return type(uint256).max;
    }

    /** @dev See {IERC4262-maxWithdraw} */
    function maxWithdraw(address owner) public view virtual override returns (uint256) {
        return _convertToAssets(balanceOf(owner), Math.Rounding.Down);
    }

    /** @dev See {IERC4262-maxRedeem} */
    function maxRedeem(address owner) public view virtual override returns (uint256) {
        return balanceOf(owner);
    }

    /** @dev See {IERC4262-previewDeposit} */
    function previewDeposit(uint256 assets) public view virtual override returns (uint256) {
        return _convertToShares(assets, Math.Rounding.Down);
    }

    /** @dev See {IERC4262-previewMint} */
    function previewMint(uint256 shares) public view virtual override returns (uint256) {
        return _convertToAssets(shares, Math.Rounding.Up);
    }

    /** @dev See {IERC4262-previewWithdraw} */
    function previewWithdraw(uint256 assets) public view virtual override returns (uint256) {
        return _convertToShares(assets, Math.Rounding.Up);
    }

    /** @dev See {IERC4262-previewRedeem} */
    function previewRedeem(uint256 shares) public view virtual override returns (uint256) {
        return _convertToAssets(shares, Math.Rounding.Down);
    }

    /** @dev See {IERC4262-deposit} */
    function deposit(uint256 assets, address receiver) public virtual override returns (uint256) {
        require(assets <= maxDeposit(receiver), "ERC4626: deposit more than max");

        uint256 shares = previewDeposit(assets);
        _deposit(_msgSender(), receiver, assets, shares);

        return shares;
    }

    /** @dev See {IERC4262-mint} */
    function mint(uint256 shares, address receiver) public virtual override returns (uint256) {
        require(shares <= maxMint(receiver), "ERC4626: mint more than max");

        uint256 assets = previewMint(shares);
        _deposit(_msgSender(), receiver, assets, shares);

        return assets;
    }

    /** @dev See {IERC4262-withdraw} */
    function withdraw(
        uint256 assets,
        address receiver,
        address owner
    ) public virtual override returns (uint256) {
        require(assets <= maxWithdraw(owner), "ERC4626: withdraw more than max");

        uint256 shares = previewWithdraw(assets);
        _withdraw(_msgSender(), receiver, owner, assets, shares);

        return shares;
    }

    /** @dev See {IERC4262-redeem} */
    function redeem(
        uint256 shares,
        address receiver,
        address owner
    ) public virtual override returns (uint256) {
        require(shares <= maxRedeem(owner), "ERC4626: redeem more than max");

        uint256 assets = previewRedeem(shares);
        _withdraw(_msgSender(), receiver, owner, assets, shares);

        return assets;
    }

    /**
     * @dev Internal convertion function (from assets to shares) with support for rounding direction
     *
     * Will revert if assets > 0, totalSupply > 0 and totalAssets = 0. That corresponds to a case where any asset
     * would represent an infinite amout of shares.
     */
    function _convertToShares(uint256 assets, Math.Rounding rounding) internal view virtual returns (uint256 shares) {
        uint256 supply = totalSupply();
        return
            (assets == 0 || supply == 0)
                ? assets.mulDiv(10**decimals(), 10**_asset.decimals(), rounding)
                : assets.mulDiv(supply, totalAssets(), rounding);
    }

    /**
     * @dev Internal convertion function (from shares to assets) with support for rounding direction
     */
    function _convertToAssets(uint256 shares, Math.Rounding rounding) internal view virtual returns (uint256 assets) {
        uint256 supply = totalSupply();
        return
            (supply == 0)
                ? shares.mulDiv(10**_asset.decimals(), 10**decimals(), rounding)
                : shares.mulDiv(totalAssets(), supply, rounding);
    }

    /**
     * @dev Deposit/mint common workflow
     */
    function _deposit(
        address caller,
        address receiver,
        uint256 assets,
        uint256 shares
    ) private {
        // If _asset is ERC777, `transferFrom` can trigger a reenterancy BEFORE the transfer happens through the
        // `tokensToSend` hook. On the other hand, the `tokenReceived` hook, that is triggered after the transfer,
        // calls the vault, which is assumed not malicious.
        //
        // Conclusion: we need to do the transfer before we mint so that any reentrancy would happen before the
        // assets are transfered and before the shares are minted, which is a valid state.
        // slither-disable-next-line reentrancy-no-eth
        SafeERC20.safeTransferFrom(_asset, caller, address(this), assets);
        _mint(receiver, shares);

        emit Deposit(caller, receiver, assets, shares);
    }

    /**
     * @dev Withdraw/redeem common workflow
     */
    function _withdraw(
        address caller,
        address receiver,
        address owner,
        uint256 assets,
        uint256 shares
    ) private {
        if (caller != owner) {
            _spendAllowance(owner, caller, shares);
        }

        // If _asset is ERC777, `transfer` can trigger trigger a reentrancy AFTER the transfer happens through the
        // `tokensReceived` hook. On the other hand, the `tokensToSend` hook, that is triggered before the transfer,
        // calls the vault, which is assumed not malicious.
        //
        // Conclusion: we need to do the transfer after the burn so that any reentrancy would happen after the
        // shares are burned and after the assets are transfered, which is a valid state.
        _burn(owner, shares);
        SafeERC20.safeTransfer(_asset, receiver, assets);

        emit Withdraw(caller, receiver, owner, assets, shares);
    }

    function _isVaultCollateralized() private view returns (bool) {
        return totalAssets() > 0 || totalSupply() == 0;
    }
}


Update merkle multiproof docs with a caution note

(cherry picked from commit 8d908fe2c20503b05f888dd9f702e3fa6fa65840)

// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v4.7.0) (utils/cryptography/MerkleProof.sol)

pragma solidity ^0.8.0;

/**
 * @dev These functions deal with verification of Merkle Tree proofs.
 *
 * The proofs can be generated using the JavaScript library
 * https://github.com/miguelmota/merkletreejs[merkletreejs].
 * Note: the hashing algorithm should be keccak256 and pair sorting should be enabled.
 *
 * See `test/utils/cryptography/MerkleProof.test.js` for some examples.
 *
 * WARNING: You should avoid using leaf values that are 64 bytes long prior to
 * hashing, or use a hash function other than keccak256 for hashing leaves.
 * This is because the concatenation of a sorted pair of internal nodes in
 * the merkle tree could be reinterpreted as a leaf value.
 */
library MerkleProof {
    /**
     * @dev Returns true if a `leaf` can be proved to be a part of a Merkle tree
     * defined by `root`. For this, a `proof` must be provided, containing
     * sibling hashes on the branch from the leaf to the root of the tree. Each
     * pair of leaves and each pair of pre-images are assumed to be sorted.
     */
    function verify(
        bytes32[] memory proof,
        bytes32 root,
        bytes32 leaf
    ) internal pure returns (bool) {
        return processProof(proof, leaf) == root;
    }

    /**
     * @dev Calldata version of {verify}
     *
     * _Available since v4.7._
     */
    function verifyCalldata(
        bytes32[] calldata proof,
        bytes32 root,
        bytes32 leaf
    ) internal pure returns (bool) {
        return processProofCalldata(proof, leaf) == root;
    }

    /**
     * @dev Returns the rebuilt hash obtained by traversing a Merkle tree up
     * from `leaf` using `proof`. A `proof` is valid if and only if the rebuilt
     * hash matches the root of the tree. When processing the proof, the pairs
     * of leafs & pre-images are assumed to be sorted.
     *
     * _Available since v4.4._
     */
    function processProof(bytes32[] memory proof, bytes32 leaf) internal pure returns (bytes32) {
        bytes32 computedHash = leaf;
        for (uint256 i = 0; i < proof.length; i++) {
            computedHash = _hashPair(computedHash, proof[i]);
        }
        return computedHash;
    }

    /**
     * @dev Calldata version of {processProof}
     *
     * _Available since v4.7._
     */
    function processProofCalldata(bytes32[] calldata proof, bytes32 leaf) internal pure returns (bytes32) {
        bytes32 computedHash = leaf;
        for (uint256 i = 0; i < proof.length; i++) {
            computedHash = _hashPair(computedHash, proof[i]);
        }
        return computedHash;
    }

    /**
     * @dev Returns true if the `leaves` can be simultaneously proven to be a part of a merkle tree defined by
     * `root`, according to `proof` and `proofFlags` as described in {processMultiProof}.
     *
     * CAUTION: Not all merkle trees admit multiproofs. See {processMultiProof} for details.
     *
     * _Available since v4.7._
     */
    function multiProofVerify(
        bytes32[] memory proof,
        bool[] memory proofFlags,
        bytes32 root,
        bytes32[] memory leaves
    ) internal pure returns (bool) {
        return processMultiProof(proof, proofFlags, leaves) == root;
    }

    /**
     * @dev Calldata version of {multiProofVerify}
     *
     * CAUTION: Not all merkle trees admit multiproofs. See {processMultiProof} for details.
     *
     * _Available since v4.7._
     */
    function multiProofVerifyCalldata(
        bytes32[] calldata proof,
        bool[] calldata proofFlags,
        bytes32 root,
        bytes32[] memory leaves
    ) internal pure returns (bool) {
        return processMultiProofCalldata(proof, proofFlags, leaves) == root;
    }

    /**
     * @dev Returns the root of a tree reconstructed from `leaves` and sibling nodes in `proof`. The reconstruction
     * proceeds by incrementally reconstructing all inner nodes by combining a leaf/inner node with either another
     * leaf/inner node or a proof sibling node, depending on whether each `proofFlags` item is true or false
     * respectively.
     *
     * CAUTION: Not all merkle trees admit multiproofs. To use multiproofs, it is sufficient to ensure that: 1) the tree
     * is complete (but not necessarily perfect), 2) the leaves to be proven are in the opposite order they are in the
     * tree (i.e., as seen from right to left starting at the deepest layer and continuing at the next layer).
     *
     * _Available since v4.7._
     */
    function processMultiProof(
        bytes32[] memory proof,
        bool[] memory proofFlags,
        bytes32[] memory leaves
    ) internal pure returns (bytes32 merkleRoot) {
        // This function rebuild the root hash by traversing the tree up from the leaves. The root is rebuilt by
        // consuming and producing values on a queue. The queue starts with the `leaves` array, then goes onto the
        // `hashes` array. At the end of the process, the last hash in the `hashes` array should contain the root of
        // the merkle tree.
        uint256 leavesLen = leaves.length;
        uint256 totalHashes = proofFlags.length;

        // Check proof validity.
        require(leavesLen + proof.length - 1 == totalHashes, "MerkleProof: invalid multiproof");

        // The xxxPos values are "pointers" to the next value to consume in each array. All accesses are done using
        // `xxx[xxxPos++]`, which return the current value and increment the pointer, thus mimicking a queue's "pop".
        bytes32[] memory hashes = new bytes32[](totalHashes);
        uint256 leafPos = 0;
        uint256 hashPos = 0;
        uint256 proofPos = 0;
        // At each step, we compute the next hash using two values:
        // - a value from the "main queue". If not all leaves have been consumed, we get the next leaf, otherwise we
        //   get the next hash.
        // - depending on the flag, either another value for the "main queue" (merging branches) or an element from the
        //   `proof` array.
        for (uint256 i = 0; i < totalHashes; i++) {
            bytes32 a = leafPos < leavesLen ? leaves[leafPos++] : hashes[hashPos++];
            bytes32 b = proofFlags[i] ? leafPos < leavesLen ? leaves[leafPos++] : hashes[hashPos++] : proof[proofPos++];
            hashes[i] = _hashPair(a, b);
        }

        if (totalHashes > 0) {
            return hashes[totalHashes - 1];
        } else if (leavesLen > 0) {
            return leaves[0];
        } else {
            return proof[0];
        }
    }

    /**
     * @dev Calldata version of {processMultiProof}.
     *
     * CAUTION: Not all merkle trees admit multiproofs. See {processMultiProof} for details.
     *
     * _Available since v4.7._
     */
    function processMultiProofCalldata(
        bytes32[] calldata proof,
        bool[] calldata proofFlags,
        bytes32[] memory leaves
    ) internal pure returns (bytes32 merkleRoot) {
        // This function rebuild the root hash by traversing the tree up from the leaves. The root is rebuilt by
        // consuming and producing values on a queue. The queue starts with the `leaves` array, then goes onto the
        // `hashes` array. At the end of the process, the last hash in the `hashes` array should contain the root of
        // the merkle tree.
        uint256 leavesLen = leaves.length;
        uint256 totalHashes = proofFlags.length;

        // Check proof validity.
        require(leavesLen + proof.length - 1 == totalHashes, "MerkleProof: invalid multiproof");

        // The xxxPos values are "pointers" to the next value to consume in each array. All accesses are done using
        // `xxx[xxxPos++]`, which return the current value and increment the pointer, thus mimicking a queue's "pop".
        bytes32[] memory hashes = new bytes32[](totalHashes);
        uint256 leafPos = 0;
        uint256 hashPos = 0;
        uint256 proofPos = 0;
        // At each step, we compute the next hash using two values:
        // - a value from the "main queue". If not all leaves have been consumed, we get the next leaf, otherwise we
        //   get the next hash.
        // - depending on the flag, either another value for the "main queue" (merging branches) or an element from the
        //   `proof` array.
        for (uint256 i = 0; i < totalHashes; i++) {
            bytes32 a = leafPos < leavesLen ? leaves[leafPos++] : hashes[hashPos++];
            bytes32 b = proofFlags[i] ? leafPos < leavesLen ? leaves[leafPos++] : hashes[hashPos++] : proof[proofPos++];
            hashes[i] = _hashPair(a, b);
        }

        if (totalHashes > 0) {
            return hashes[totalHashes - 1];
        } else if (leavesLen > 0) {
            return leaves[0];
        } else {
            return proof[0];
        }
    }

    function _hashPair(bytes32 a, bytes32 b) private pure returns (bytes32) {
        return a < b ? _efficientHash(a, b) : _efficientHash(b, a);
    }

    function _efficientHash(bytes32 a, bytes32 b) private pure returns (bytes32 value) {
        /// @solidity memory-safe-assembly
        assembly {
            mstore(0x00, a)
            mstore(0x20, b)
            value := keccak256(0x00, 0x40)
        }
    }
}

// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v4.7.0) (utils/cryptography/MerkleProof.sol)

pragma solidity ^0.8.0;

/**
 * @dev These functions deal with verification of Merkle Tree proofs.
 *
 * The proofs can be generated using the JavaScript library
 * https://github.com/miguelmota/merkletreejs[merkletreejs].
 * Note: the hashing algorithm should be keccak256 and pair sorting should be enabled.
 *
 * See `test/utils/cryptography/MerkleProof.test.js` for some examples.
 *
 * WARNING: You should avoid using leaf values that are 64 bytes long prior to
 * hashing, or use a hash function other than keccak256 for hashing leaves.
 * This is because the concatenation of a sorted pair of internal nodes in
 * the merkle tree could be reinterpreted as a leaf value.
 */
library MerkleProof {
    /**
     * @dev Returns true if a `leaf` can be proved to be a part of a Merkle tree
     * defined by `root`. For this, a `proof` must be provided, containing
     * sibling hashes on the branch from the leaf to the root of the tree. Each
     * pair of leaves and each pair of pre-images are assumed to be sorted.
     */
    function verify(
        bytes32[] memory proof,
        bytes32 root,
        bytes32 leaf
    ) internal pure returns (bool) {
        return processProof(proof, leaf) == root;
    }

    /**
     * @dev Calldata version of {verify}
     *
     * _Available since v4.7._
     */
    function verifyCalldata(
        bytes32[] calldata proof,
        bytes32 root,
        bytes32 leaf
    ) internal pure returns (bool) {
        return processProofCalldata(proof, leaf) == root;
    }

    /**
     * @dev Returns the rebuilt hash obtained by traversing a Merkle tree up
     * from `leaf` using `proof`. A `proof` is valid if and only if the rebuilt
     * hash matches the root of the tree. When processing the proof, the pairs
     * of leafs & pre-images are assumed to be sorted.
     *
     * _Available since v4.4._
     */
    function processProof(bytes32[] memory proof, bytes32 leaf) internal pure returns (bytes32) {
        bytes32 computedHash = leaf;
        for (uint256 i = 0; i < proof.length; i++) {
            computedHash = _hashPair(computedHash, proof[i]);
        }
        return computedHash;
    }

    /**
     * @dev Calldata version of {processProof}
     *
     * _Available since v4.7._
     */
    function processProofCalldata(bytes32[] calldata proof, bytes32 leaf) internal pure returns (bytes32) {
        bytes32 computedHash = leaf;
        for (uint256 i = 0; i < proof.length; i++) {
            computedHash = _hashPair(computedHash, proof[i]);
        }
        return computedHash;
    }

    /**
     * @dev Returns true if the `leaves` can be proved to be a part of a Merkle tree defined by
     * `root`, according to `proof` and `proofFlags` as described in {processMultiProof}.
     *
     * _Available since v4.7._
     */
    function multiProofVerify(
        bytes32[] memory proof,
        bool[] memory proofFlags,
        bytes32 root,
        bytes32[] memory leaves
    ) internal pure returns (bool) {
        return processMultiProof(proof, proofFlags, leaves) == root;
    }

    /**
     * @dev Calldata version of {multiProofVerify}
     *
     * _Available since v4.7._
     */
    function multiProofVerifyCalldata(
        bytes32[] calldata proof,
        bool[] calldata proofFlags,
        bytes32 root,
        bytes32[] memory leaves
    ) internal pure returns (bool) {
        return processMultiProofCalldata(proof, proofFlags, leaves) == root;
    }

    /**
     * @dev Returns the root of a tree reconstructed from `leaves` and the sibling nodes in `proof`,
     * consuming from one or the other at each step according to the instructions given by
     * `proofFlags`.
     *
     * _Available since v4.7._
     */
    function processMultiProof(
        bytes32[] memory proof,
        bool[] memory proofFlags,
        bytes32[] memory leaves
    ) internal pure returns (bytes32 merkleRoot) {
        // This function rebuild the root hash by traversing the tree up from the leaves. The root is rebuilt by
        // consuming and producing values on a queue. The queue starts with the `leaves` array, then goes onto the
        // `hashes` array. At the end of the process, the last hash in the `hashes` array should contain the root of
        // the merkle tree.
        uint256 leavesLen = leaves.length;
        uint256 totalHashes = proofFlags.length;

        // Check proof validity.
        require(leavesLen + proof.length - 1 == totalHashes, "MerkleProof: invalid multiproof");

        // The xxxPos values are "pointers" to the next value to consume in each array. All accesses are done using
        // `xxx[xxxPos++]`, which return the current value and increment the pointer, thus mimicking a queue's "pop".
        bytes32[] memory hashes = new bytes32[](totalHashes);
        uint256 leafPos = 0;
        uint256 hashPos = 0;
        uint256 proofPos = 0;
        // At each step, we compute the next hash using two values:
        // - a value from the "main queue". If not all leaves have been consumed, we get the next leaf, otherwise we
        //   get the next hash.
        // - depending on the flag, either another value for the "main queue" (merging branches) or an element from the
        //   `proof` array.
        for (uint256 i = 0; i < totalHashes; i++) {
            bytes32 a = leafPos < leavesLen ? leaves[leafPos++] : hashes[hashPos++];
            bytes32 b = proofFlags[i] ? leafPos < leavesLen ? leaves[leafPos++] : hashes[hashPos++] : proof[proofPos++];
            hashes[i] = _hashPair(a, b);
        }

        if (totalHashes > 0) {
            return hashes[totalHashes - 1];
        } else if (leavesLen > 0) {
            return leaves[0];
        } else {
            return proof[0];
        }
    }

    /**
     * @dev Calldata version of {processMultiProof}
     *
     * _Available since v4.7._
     */
    function processMultiProofCalldata(
        bytes32[] calldata proof,
        bool[] calldata proofFlags,
        bytes32[] memory leaves
    ) internal pure returns (bytes32 merkleRoot) {
        // This function rebuild the root hash by traversing the tree up from the leaves. The root is rebuilt by
        // consuming and producing values on a queue. The queue starts with the `leaves` array, then goes onto the
        // `hashes` array. At the end of the process, the last hash in the `hashes` array should contain the root of
        // the merkle tree.
        uint256 leavesLen = leaves.length;
        uint256 totalHashes = proofFlags.length;

        // Check proof validity.
        require(leavesLen + proof.length - 1 == totalHashes, "MerkleProof: invalid multiproof");

        // The xxxPos values are "pointers" to the next value to consume in each array. All accesses are done using
        // `xxx[xxxPos++]`, which return the current value and increment the pointer, thus mimicking a queue's "pop".
        bytes32[] memory hashes = new bytes32[](totalHashes);
        uint256 leafPos = 0;
        uint256 hashPos = 0;
        uint256 proofPos = 0;
        // At each step, we compute the next hash using two values:
        // - a value from the "main queue". If not all leaves have been consumed, we get the next leaf, otherwise we
        //   get the next hash.
        // - depending on the flag, either another value for the "main queue" (merging branches) or an element from the
        //   `proof` array.
        for (uint256 i = 0; i < totalHashes; i++) {
            bytes32 a = leafPos < leavesLen ? leaves[leafPos++] : hashes[hashPos++];
            bytes32 b = proofFlags[i] ? leafPos < leavesLen ? leaves[leafPos++] : hashes[hashPos++] : proof[proofPos++];
            hashes[i] = _hashPair(a, b);
        }

        if (totalHashes > 0) {
            return hashes[totalHashes - 1];
        } else if (leavesLen > 0) {
            return leaves[0];
        } else {
            return proof[0];
        }
    }

    function _hashPair(bytes32 a, bytes32 b) private pure returns (bytes32) {
        return a < b ? _efficientHash(a, b) : _efficientHash(b, a);
    }

    function _efficientHash(bytes32 a, bytes32 b) private pure returns (bytes32 value) {
        /// @solidity memory-safe-assembly
        assembly {
            mstore(0x00, a)
            mstore(0x20, b)
            value := keccak256(0x00, 0x40)
        }
    }
}