// SPDX-License-Identifier: MIT
pragma solidity ^0.8.4;

import {PoseidonT3} from "poseidon-solidity/PoseidonT3.sol";

// Each incremental tree has certain properties and data that will
// be used to add new leaves.
struct IncrementalTreeData {
    uint256 depth; // Depth of the tree (levels - 1).
    uint256 root; // Root hash of the tree.
    uint256 numberOfLeaves; // Number of leaves of the tree.
    mapping(uint256 => uint256) zeroes; // Zero hashes used for empty nodes (level -> zero hash).
    // The nodes of the subtrees used in the last addition of a leaf (level -> [left node, right node]).
    mapping(uint256 => uint256[2]) lastSubtrees; // Caching these values is essential to efficient appends.
    bool useDefaultZeroes;
}

/// @title Incremental binary Merkle tree.
/// @dev The incremental tree allows to calculate the root hash each time a leaf is added, ensuring
/// the integrity of the tree.
library IncrementalBinaryTree {
    uint8 internal constant MAX_DEPTH = 32;
    uint256 internal constant SNARK_SCALAR_FIELD =
        21888242871839275222246405745257275088548364400416034343698204186575808495617;

    uint256 public constant Z_0 = 0;
    uint256 public constant Z_1 = 14744269619966411208579211824598458697587494354926760081771325075741142829156;
    uint256 public constant Z_2 = 7423237065226347324353380772367382631490014989348495481811164164159255474657;
    uint256 public constant Z_3 = 11286972368698509976183087595462810875513684078608517520839298933882497716792;
    uint256 public constant Z_4 = 3607627140608796879659380071776844901612302623152076817094415224584923813162;
    uint256 public constant Z_5 = 19712377064642672829441595136074946683621277828620209496774504837737984048981;
    uint256 public constant Z_6 = 20775607673010627194014556968476266066927294572720319469184847051418138353016;
    uint256 public constant Z_7 = 3396914609616007258851405644437304192397291162432396347162513310381425243293;
    uint256 public constant Z_8 = 21551820661461729022865262380882070649935529853313286572328683688269863701601;
    uint256 public constant Z_9 = 6573136701248752079028194407151022595060682063033565181951145966236778420039;
    uint256 public constant Z_10 = 12413880268183407374852357075976609371175688755676981206018884971008854919922;
    uint256 public constant Z_11 = 14271763308400718165336499097156975241954733520325982997864342600795471836726;
    uint256 public constant Z_12 = 20066985985293572387227381049700832219069292839614107140851619262827735677018;
    uint256 public constant Z_13 = 9394776414966240069580838672673694685292165040808226440647796406499139370960;
    uint256 public constant Z_14 = 11331146992410411304059858900317123658895005918277453009197229807340014528524;
    uint256 public constant Z_15 = 15819538789928229930262697811477882737253464456578333862691129291651619515538;
    uint256 public constant Z_16 = 19217088683336594659449020493828377907203207941212636669271704950158751593251;
    uint256 public constant Z_17 = 21035245323335827719745544373081896983162834604456827698288649288827293579666;
    uint256 public constant Z_18 = 6939770416153240137322503476966641397417391950902474480970945462551409848591;
    uint256 public constant Z_19 = 10941962436777715901943463195175331263348098796018438960955633645115732864202;
    uint256 public constant Z_20 = 15019797232609675441998260052101280400536945603062888308240081994073687793470;
    uint256 public constant Z_21 = 11702828337982203149177882813338547876343922920234831094975924378932809409969;
    uint256 public constant Z_22 = 11217067736778784455593535811108456786943573747466706329920902520905755780395;
    uint256 public constant Z_23 = 16072238744996205792852194127671441602062027943016727953216607508365787157389;
    uint256 public constant Z_24 = 17681057402012993898104192736393849603097507831571622013521167331642182653248;
    uint256 public constant Z_25 = 21694045479371014653083846597424257852691458318143380497809004364947786214945;
    uint256 public constant Z_26 = 8163447297445169709687354538480474434591144168767135863541048304198280615192;
    uint256 public constant Z_27 = 14081762237856300239452543304351251708585712948734528663957353575674639038357;
    uint256 public constant Z_28 = 16619959921569409661790279042024627172199214148318086837362003702249041851090;
    uint256 public constant Z_29 = 7022159125197495734384997711896547675021391130223237843255817587255104160365;
    uint256 public constant Z_30 = 4114686047564160449611603615418567457008101555090703535405891656262658644463;
    uint256 public constant Z_31 = 12549363297364877722388257367377629555213421373705596078299904496781819142130;
    uint256 public constant Z_32 = 21443572485391568159800782191812935835534334817699172242223315142338162256601;

    function defaultZero(uint256 index) public pure returns (uint256) {
        if (index == 0) return Z_0;
        if (index == 1) return Z_1;
        if (index == 2) return Z_2;
        if (index == 3) return Z_3;
        if (index == 4) return Z_4;
        if (index == 5) return Z_5;
        if (index == 6) return Z_6;
        if (index == 7) return Z_7;
        if (index == 8) return Z_8;
        if (index == 9) return Z_9;
        if (index == 10) return Z_10;
        if (index == 11) return Z_11;
        if (index == 12) return Z_12;
        if (index == 13) return Z_13;
        if (index == 14) return Z_14;
        if (index == 15) return Z_15;
        if (index == 16) return Z_16;
        if (index == 17) return Z_17;
        if (index == 18) return Z_18;
        if (index == 19) return Z_19;
        if (index == 20) return Z_20;
        if (index == 21) return Z_21;
        if (index == 22) return Z_22;
        if (index == 23) return Z_23;
        if (index == 24) return Z_24;
        if (index == 25) return Z_25;
        if (index == 26) return Z_26;
        if (index == 27) return Z_27;
        if (index == 28) return Z_28;
        if (index == 29) return Z_29;
        if (index == 30) return Z_30;
        if (index == 31) return Z_31;
        if (index == 32) return Z_32;
        revert("IncrementalBinaryTree: defaultZero bad index");
    }

    /// @dev Initializes a tree.
    /// @param self: Tree data.
    /// @param depth: Depth of the tree.
    /// @param zero: Zero value to be used.
    function init(
        IncrementalTreeData storage self,
        uint256 depth,
        uint256 zero
    ) public {
        require(zero < SNARK_SCALAR_FIELD, "IncrementalBinaryTree: leaf must be < SNARK_SCALAR_FIELD");
        require(depth > 0 && depth <= MAX_DEPTH, "IncrementalBinaryTree: tree depth must be between 1 and 32");

        self.depth = depth;

        for (uint8 i = 0; i < depth; ) {
            self.zeroes[i] = zero;
            zero = PoseidonT3.hash([zero, zero]);

            unchecked {
                ++i;
            }
        }

        self.root = zero;
    }

    function initWithDefaultZeroes(IncrementalTreeData storage self, uint256 depth) public {
        require(depth > 0 && depth <= MAX_DEPTH, "IncrementalBinaryTree: tree depth must be between 1 and 32");

        self.depth = depth;
        self.useDefaultZeroes = true;

        self.root = defaultZero(depth);
    }

    /// @dev Inserts a leaf in the tree.
    /// @param self: Tree data.
    /// @param leaf: Leaf to be inserted.
    function insert(IncrementalTreeData storage self, uint256 leaf) public returns (uint256) {
        uint256 depth = self.depth;

        require(leaf < SNARK_SCALAR_FIELD, "IncrementalBinaryTree: leaf must be < SNARK_SCALAR_FIELD");
        require(self.numberOfLeaves < 2**depth, "IncrementalBinaryTree: tree is full");

        uint256 index = self.numberOfLeaves;
        uint256 hash = leaf;
        bool useDefaultZeroes = self.useDefaultZeroes;

        for (uint8 i = 0; i < depth; ) {
            if (index & 1 == 0) {
                self.lastSubtrees[i] = [hash, useDefaultZeroes ? defaultZero(i) : self.zeroes[i]];
            } else {
                self.lastSubtrees[i][1] = hash;
            }

            hash = PoseidonT3.hash(self.lastSubtrees[i]);
            index >>= 1;

            unchecked {
                ++i;
            }
        }

        self.root = hash;
        self.numberOfLeaves += 1;
        return hash;
    }

    /// @dev Updates a leaf in the tree.
    /// @param self: Tree data.
    /// @param leaf: Leaf to be updated.
    /// @param newLeaf: New leaf.
    /// @param proofSiblings: Array of the sibling nodes of the proof of membership.
    /// @param proofPathIndices: Path of the proof of membership.
    function update(
        IncrementalTreeData storage self,
        uint256 leaf,
        uint256 newLeaf,
        uint256[] calldata proofSiblings,
        uint8[] calldata proofPathIndices
    ) public {
        require(newLeaf != leaf, "IncrementalBinaryTree: new leaf cannot be the same as the old one");
        require(newLeaf < SNARK_SCALAR_FIELD, "IncrementalBinaryTree: new leaf must be < SNARK_SCALAR_FIELD");
        require(
            verify(self, leaf, proofSiblings, proofPathIndices),
            "IncrementalBinaryTree: leaf is not part of the tree"
        );

        uint256 depth = self.depth;
        uint256 hash = newLeaf;
        uint256 updateIndex;

        for (uint8 i = 0; i < depth; ) {
            updateIndex |= uint256(proofPathIndices[i]) << uint256(i);

            if (proofPathIndices[i] == 0) {
                if (proofSiblings[i] == self.lastSubtrees[i][1]) {
                    self.lastSubtrees[i][0] = hash;
                }

                hash = PoseidonT3.hash([hash, proofSiblings[i]]);
            } else {
                if (proofSiblings[i] == self.lastSubtrees[i][0]) {
                    self.lastSubtrees[i][1] = hash;
                }

                hash = PoseidonT3.hash([proofSiblings[i], hash]);
            }

            unchecked {
                ++i;
            }
        }
        require(updateIndex < self.numberOfLeaves, "IncrementalBinaryTree: leaf index out of range");

        self.root = hash;
    }

    /// @dev Removes a leaf from the tree.
    /// @param self: Tree data.
    /// @param leaf: Leaf to be removed.
    /// @param proofSiblings: Array of the sibling nodes of the proof of membership.
    /// @param proofPathIndices: Path of the proof of membership.
    function remove(
        IncrementalTreeData storage self,
        uint256 leaf,
        uint256[] calldata proofSiblings,
        uint8[] calldata proofPathIndices
    ) public {
        update(self, leaf, self.useDefaultZeroes ? Z_0 : self.zeroes[0], proofSiblings, proofPathIndices);
    }

    /// @dev Verify if the path is correct and the leaf is part of the tree.
    /// @param self: Tree data.
    /// @param leaf: Leaf to be removed.
    /// @param proofSiblings: Array of the sibling nodes of the proof of membership.
    /// @param proofPathIndices: Path of the proof of membership.
    /// @return True or false.
    function verify(
        IncrementalTreeData storage self,
        uint256 leaf,
        uint256[] calldata proofSiblings,
        uint8[] calldata proofPathIndices
    ) private view returns (bool) {
        require(leaf < SNARK_SCALAR_FIELD, "IncrementalBinaryTree: leaf must be < SNARK_SCALAR_FIELD");
        uint256 depth = self.depth;
        require(
            proofPathIndices.length == depth && proofSiblings.length == depth,
            "IncrementalBinaryTree: length of path is not correct"
        );

        uint256 hash = leaf;

        for (uint8 i = 0; i < depth; ) {
            require(
                proofSiblings[i] < SNARK_SCALAR_FIELD,
                "IncrementalBinaryTree: sibling node must be < SNARK_SCALAR_FIELD"
            );

            require(
                proofPathIndices[i] == 1 || proofPathIndices[i] == 0,
                "IncrementalBinaryTree: path index is neither 0 nor 1"
            );

            if (proofPathIndices[i] == 0) {
                hash = PoseidonT3.hash([hash, proofSiblings[i]]);
            } else {
                hash = PoseidonT3.hash([proofSiblings[i], hash]);
            }

            unchecked {
                ++i;
            }
        }

        return hash == self.root;
    }
}