// SPDX-License-Identifier: MIT
pragma solidity ^0.8.0;

import 'poseidon-solidity/PoseidonT3.sol';

struct LazyTreeData {
    uint32 maxIndex;
    uint40 numberOfLeaves;
    mapping(uint256 => uint256) elements;
}

// TODO: update doc
/// @title LazyMerkleTree
library LazyMerkleTree {
    uint256 internal constant SNARK_SCALAR_FIELD =
        21888242871839275222246405745257275088548364400416034343698204186575808495617;
    uint8 internal constant MAX_DEPTH = 32;
    uint40 internal constant MAX_INDEX = (1 << 32) - 1;

    function init(LazyTreeData storage self, uint8 depth) public {
        require(depth <= MAX_DEPTH, 'LazyMerkleTree: Tree too large');
        self.maxIndex = uint32((1 << depth) - 1);
        self.numberOfLeaves = 0;
    }

    function reset(LazyTreeData storage self) public {
        self.numberOfLeaves = 0;
    }

    function indexForElement(
        uint8 level,
        uint40 index
    ) public pure returns (uint40) {
        // store the elements sparsely
        return MAX_INDEX * level + index;
    }

    function insert(LazyTreeData storage self, uint256 leaf) public {
        uint40 index = self.numberOfLeaves;
        self.numberOfLeaves = index + 1;
        require(
            leaf < SNARK_SCALAR_FIELD,
            'LazyMerkleTree: leaf must be < SNARK_SCALAR_FIELD'
        );
        require(index < self.maxIndex, 'LazyMerkleTree: tree is full');

        uint256 hash = leaf;

        for (uint8 i = 0; true; ) {
            self.elements[indexForElement(i, index)] = hash;
            // it's a left element so we don't hash until there's a right element
            if (index & 1 == 0) break;
            uint40 elementIndex = indexForElement(i, index - 1);
            hash = PoseidonT3.hash([self.elements[elementIndex], hash]);
            unchecked {
                index >>= 1;
                i++;
            }
        }
    }

    function update(
        LazyTreeData storage self,
        uint256 leaf,
        uint40 index
    ) public {
        require(
            leaf < SNARK_SCALAR_FIELD,
            'LazyMerkleTree: leaf must be < SNARK_SCALAR_FIELD'
        );
        uint40 numberOfLeaves = self.numberOfLeaves;
        require(index < numberOfLeaves, 'LazyMerkleTree: leaf must exist');

        uint256 hash = leaf;

        for (uint8 i = 0; true; ) {
            self.elements[indexForElement(i, index)] = hash;
            uint256 levelCount = numberOfLeaves >> (i + 1);
            if (levelCount <= index >> 1) break;
            if (index & 1 == 0) {
                uint40 elementIndex = indexForElement(i, index + 1);
                hash = PoseidonT3.hash([hash, self.elements[elementIndex]]);
            } else {
                uint40 elementIndex = indexForElement(i, index - 1);
                hash = PoseidonT3.hash([self.elements[elementIndex], hash]);
            }
            unchecked {
                index >>= 1;
                i++;
            }
        }
    }

    function root(
        LazyTreeData storage self,
        uint8 depth
    ) public view returns (uint256) {
        // this will always short circuit if self.numberOfLeaves == 0
        uint40 numberOfLeaves = self.numberOfLeaves;
        if (numberOfLeaves == 0) return defaultZero(depth);
        uint40 index = numberOfLeaves - 1;

        uint256[MAX_DEPTH + 1] memory levels;

        if (index & 1 == 0) {
            levels[0] = self.elements[indexForElement(0, index)];
        } else {
            levels[0] = defaultZero(0);
        }

        for (uint8 i = 0; i < depth; ) {
            if (index & 1 == 0) {
                levels[i + 1] = PoseidonT3.hash([levels[i], defaultZero(i)]);
            } else {
                uint256 levelCount = (numberOfLeaves) >> (i + 1);
                if (levelCount > index >> 1) {
                    uint256 parent = self.elements[
                        indexForElement(i + 1, index >> 1)
                    ];
                    levels[i + 1] = parent;
                } else {
                    uint256 sibling = self.elements[
                        indexForElement(i, index - 1)
                    ];
                    levels[i + 1] = PoseidonT3.hash([sibling, levels[i]]);
                }
            }
            unchecked {
                index >>= 1;
                i++;
            }
        }
        return levels[depth];
    }

    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(uint8 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('LazyMerkleTree: defaultZero bad index');
    }
}