Merkle.sol

// SPDX-License-Identifier: MIT OR Apache-2.0
pragma solidity >=0.6.11;

// work based on eth2 deposit contract, which is used under CC0-1.0

/**
 * @title MerkleLib
 * @author Illusory Systems Inc.
 * @notice An incremental merkle tree modeled on the eth2 deposit contract.
 **/
library MerkleLib {
    uint256 internal constant TREE_DEPTH = 32;
    uint256 internal constant MAX_LEAVES = 2**TREE_DEPTH - 1;

    /**
     * @notice Struct representing incremental merkle tree. Contains current
     * branch and the number of inserted leaves in the tree.
     **/
    struct Tree {
        bytes32[TREE_DEPTH] branch;
        uint256 count;
    }

    /**
     * @notice Inserts `_node` into merkle tree
     * @dev Reverts if tree is full
     * @param _node Element to insert into tree
     **/
    function insert(Tree storage _tree, bytes32 _node) internal {
        require(_tree.count < MAX_LEAVES, "merkle tree full");

        _tree.count += 1;
        uint256 size = _tree.count;
        for (uint256 i = 0; i < TREE_DEPTH; i++) {
            if ((size & 1) == 1) {
                _tree.branch[i] = _node;
                return;
            }
            _node = keccak256(abi.encodePacked(_tree.branch[i], _node));
            size /= 2;
        }
        // As the loop should always end prematurely with the `return` statement,
        // this code should be unreachable. We assert `false` just to be safe.
        assert(false);
    }

    /**
     * @notice Calculates and returns`_tree`'s current root given array of zero
     * hashes
     * @param _zeroes Array of zero hashes
     * @return _current Calculated root of `_tree`
     **/
    function rootWithCtx(Tree storage _tree, bytes32[TREE_DEPTH] memory _zeroes)
        internal
        view
        returns (bytes32 _current)
    {
        uint256 _index = _tree.count;

        for (uint256 i = 0; i < TREE_DEPTH; i++) {
            uint256 _ithBit = (_index >> i) & 0x01;
            bytes32 _next = _tree.branch[i];
            if (_ithBit == 1) {
                _current = keccak256(abi.encodePacked(_next, _current));
            } else {
                _current = keccak256(abi.encodePacked(_current, _zeroes[i]));
            }
        }
    }

    /// @notice Calculates and returns`_tree`'s current root
    function root(Tree storage _tree) internal view returns (bytes32) {
        return rootWithCtx(_tree, zeroHashes());
    }

    /// @notice Returns array of TREE_DEPTH zero hashes
    /// @return _zeroes Array of TREE_DEPTH zero hashes
    function zeroHashes()
        internal
        pure
        returns (bytes32[TREE_DEPTH] memory _zeroes)
    {
        _zeroes[0] = Z_0;
        _zeroes[1] = Z_1;
        _zeroes[2] = Z_2;
        _zeroes[3] = Z_3;
        _zeroes[4] = Z_4;
        _zeroes[5] = Z_5;
        _zeroes[6] = Z_6;
        _zeroes[7] = Z_7;
        _zeroes[8] = Z_8;
        _zeroes[9] = Z_9;
        _zeroes[10] = Z_10;
        _zeroes[11] = Z_11;
        _zeroes[12] = Z_12;
        _zeroes[13] = Z_13;
        _zeroes[14] = Z_14;
        _zeroes[15] = Z_15;
        _zeroes[16] = Z_16;
        _zeroes[17] = Z_17;
        _zeroes[18] = Z_18;
        _zeroes[19] = Z_19;
        _zeroes[20] = Z_20;
        _zeroes[21] = Z_21;
        _zeroes[22] = Z_22;
        _zeroes[23] = Z_23;
        _zeroes[24] = Z_24;
        _zeroes[25] = Z_25;
        _zeroes[26] = Z_26;
        _zeroes[27] = Z_27;
        _zeroes[28] = Z_28;
        _zeroes[29] = Z_29;
        _zeroes[30] = Z_30;
        _zeroes[31] = Z_31;
    }

    /**
     * @notice Calculates and returns the merkle root for the given leaf
     * `_item`, a merkle branch, and the index of `_item` in the tree.
     * @param _item Merkle leaf
     * @param _branch Merkle proof
     * @param _index Index of `_item` in tree
     * @return _current Calculated merkle root
     **/
    function branchRoot(
        bytes32 _item,
        bytes32[TREE_DEPTH] memory _branch,
        uint256 _index
    ) internal pure returns (bytes32 _current) {
        _current = _item;

        for (uint256 i = 0; i < TREE_DEPTH; i++) {
            uint256 _ithBit = (_index >> i) & 0x01;
            bytes32 _next = _branch[i];
            if (_ithBit == 1) {
                _current = keccak256(abi.encodePacked(_next, _current));
            } else {
                _current = keccak256(abi.encodePacked(_current, _next));
            }
        }
    }

    // keccak256 zero hashes
    bytes32 internal constant Z_0 =
        hex"0000000000000000000000000000000000000000000000000000000000000000";
    bytes32 internal constant Z_1 =
        hex"ad3228b676f7d3cd4284a5443f17f1962b36e491b30a40b2405849e597ba5fb5";
    bytes32 internal constant Z_2 =
        hex"b4c11951957c6f8f642c4af61cd6b24640fec6dc7fc607ee8206a99e92410d30";
    bytes32 internal constant Z_3 =
        hex"21ddb9a356815c3fac1026b6dec5df3124afbadb485c9ba5a3e3398a04b7ba85";
    bytes32 internal constant Z_4 =
        hex"e58769b32a1beaf1ea27375a44095a0d1fb664ce2dd358e7fcbfb78c26a19344";
    bytes32 internal constant Z_5 =
        hex"0eb01ebfc9ed27500cd4dfc979272d1f0913cc9f66540d7e8005811109e1cf2d";
    bytes32 internal constant Z_6 =
        hex"887c22bd8750d34016ac3c66b5ff102dacdd73f6b014e710b51e8022af9a1968";
    bytes32 internal constant Z_7 =
        hex"ffd70157e48063fc33c97a050f7f640233bf646cc98d9524c6b92bcf3ab56f83";
    bytes32 internal constant Z_8 =
        hex"9867cc5f7f196b93bae1e27e6320742445d290f2263827498b54fec539f756af";
    bytes32 internal constant Z_9 =
        hex"cefad4e508c098b9a7e1d8feb19955fb02ba9675585078710969d3440f5054e0";
    bytes32 internal constant Z_10 =
        hex"f9dc3e7fe016e050eff260334f18a5d4fe391d82092319f5964f2e2eb7c1c3a5";
    bytes32 internal constant Z_11 =
        hex"f8b13a49e282f609c317a833fb8d976d11517c571d1221a265d25af778ecf892";
    bytes32 internal constant Z_12 =
        hex"3490c6ceeb450aecdc82e28293031d10c7d73bf85e57bf041a97360aa2c5d99c";
    bytes32 internal constant Z_13 =
        hex"c1df82d9c4b87413eae2ef048f94b4d3554cea73d92b0f7af96e0271c691e2bb";
    bytes32 internal constant Z_14 =
        hex"5c67add7c6caf302256adedf7ab114da0acfe870d449a3a489f781d659e8becc";
    bytes32 internal constant Z_15 =
        hex"da7bce9f4e8618b6bd2f4132ce798cdc7a60e7e1460a7299e3c6342a579626d2";
    bytes32 internal constant Z_16 =
        hex"2733e50f526ec2fa19a22b31e8ed50f23cd1fdf94c9154ed3a7609a2f1ff981f";
    bytes32 internal constant Z_17 =
        hex"e1d3b5c807b281e4683cc6d6315cf95b9ade8641defcb32372f1c126e398ef7a";
    bytes32 internal constant Z_18 =
        hex"5a2dce0a8a7f68bb74560f8f71837c2c2ebbcbf7fffb42ae1896f13f7c7479a0";
    bytes32 internal constant Z_19 =
        hex"b46a28b6f55540f89444f63de0378e3d121be09e06cc9ded1c20e65876d36aa0";
    bytes32 internal constant Z_20 =
        hex"c65e9645644786b620e2dd2ad648ddfcbf4a7e5b1a3a4ecfe7f64667a3f0b7e2";
    bytes32 internal constant Z_21 =
        hex"f4418588ed35a2458cffeb39b93d26f18d2ab13bdce6aee58e7b99359ec2dfd9";
    bytes32 internal constant Z_22 =
        hex"5a9c16dc00d6ef18b7933a6f8dc65ccb55667138776f7dea101070dc8796e377";
    bytes32 internal constant Z_23 =
        hex"4df84f40ae0c8229d0d6069e5c8f39a7c299677a09d367fc7b05e3bc380ee652";
    bytes32 internal constant Z_24 =
        hex"cdc72595f74c7b1043d0e1ffbab734648c838dfb0527d971b602bc216c9619ef";
    bytes32 internal constant Z_25 =
        hex"0abf5ac974a1ed57f4050aa510dd9c74f508277b39d7973bb2dfccc5eeb0618d";
    bytes32 internal constant Z_26 =
        hex"b8cd74046ff337f0a7bf2c8e03e10f642c1886798d71806ab1e888d9e5ee87d0";
    bytes32 internal constant Z_27 =
        hex"838c5655cb21c6cb83313b5a631175dff4963772cce9108188b34ac87c81c41e";
    bytes32 internal constant Z_28 =
        hex"662ee4dd2dd7b2bc707961b1e646c4047669dcb6584f0d8d770daf5d7e7deb2e";
    bytes32 internal constant Z_29 =
        hex"388ab20e2573d171a88108e79d820e98f26c0b84aa8b2f4aa4968dbb818ea322";
    bytes32 internal constant Z_30 =
        hex"93237c50ba75ee485f4c22adf2f741400bdf8d6a9cc7df7ecae576221665d735";
    bytes32 internal constant Z_31 =
        hex"8448818bb4ae4562849e949e17ac16e0be16688e156b5cf15e098c627c0056a9";
}