feat: add Quorum contract

- Special thanks to @ZzzzHui for helping with gas optimizations!

onchain/rollups/.changeset/lovely-carpets-change.md

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+---
+"@cartesi/rollups": minor
+---
+
+Added `Quorum` consensus contract.

onchain/rollups/contracts/consensus/quorum/Quorum.sol

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+// (c) Cartesi and individual authors (see AUTHORS)
+// SPDX-License-Identifier: Apache-2.0 (see LICENSE)
+
+pragma solidity ^0.8.8;
+
+import {BitMaps} from "@openzeppelin/contracts/utils/structs/BitMaps.sol";
+
+import {AbstractConsensus} from "../AbstractConsensus.sol";
+import {InputRange} from "../../common/InputRange.sol";
+
+/// @notice A consensus model controlled by a small, immutable set of `n` validators.
+/// @notice You can know the value of `n` by calling the `numOfValidators` function.
+/// @notice Upon construction, each validator is assigned a unique number between 1 and `n`.
+/// These numbers are used internally instead of addresses for optimization reasons.
+/// @notice You can list the validators in the quorum by calling the `validatorById`
+/// function for each ID from 1 to `n`.
+contract Quorum is AbstractConsensus {
+    using BitMaps for BitMaps.BitMap;
+
+    /// @notice The total number of validators.
+    /// @notice See the `numOfValidators` function.
+    uint256 private immutable _numOfValidators;
+
+    /// @notice Validator IDs indexed by address.
+    /// @notice See the `validatorId` function.
+    /// @dev Non-validators are assigned to ID zero.
+    /// @dev Validators have IDs greater than zero.
+    mapping(address => uint256) private _validatorId;
+
+    /// @notice Validator addresses indexed by ID.
+    /// @notice See the `validatorById` function.
+    /// @dev Invalid IDs are assigned to address zero.
+    mapping(uint256 => address) private _validatorById;
+
+    /// @notice Votes in favor of a particular claim.
+    /// @param inFavorCount The number of validators in favor of the claim
+    /// @param inFavorById The set of validators in favor of the claim
+    /// @dev `inFavorById` is a bitmap indexed by validator IDs.
+    struct Votes {
+        uint256 inFavorCount;
+        BitMaps.BitMap inFavorById;
+    }
+
+    /// @notice Votes indexed by claim.
+    /// @dev See the `numOfValidatorsInFavorOf` and `isValidatorInFavorOf` functions.
+    mapping(address => mapping(uint256 => mapping(uint256 => mapping(bytes32 => Votes))))
+        private _votes;
+
+    /// @param validators The array of validator addresses
+    /// @dev Duplicates in the `validators` array are ignored.
+    constructor(address[] memory validators) {
+        uint256 n;
+        for (uint256 i; i < validators.length; ++i) {
+            address validator = validators[i];
+            if (_validatorId[validator] == 0) {
+                uint256 id = ++n;
+                _validatorId[validator] = id;
+                _validatorById[id] = validator;
+            }
+        }
+        _numOfValidators = n;
+    }
+
+    /// @notice Submit a claim.
+    /// @notice If the majority of the quorum submit a claim, it is accepted.
+    /// @param application The application address
+    /// @param r The input range
+    /// @param epochHash The epoch hash
+    /// @dev Can only be called by a validator.
+    function submitClaim(
+        address application,
+        InputRange calldata r,
+        bytes32 epochHash
+    ) external {
+        uint256 id = _validatorId[msg.sender];
+        require(id > 0, "Quorum: caller is not validator");
+
+        emit ClaimSubmission(msg.sender, application, r, epochHash);
+
+        Votes storage votes = _getVotes(application, r, epochHash);
+
+        if (!votes.inFavorById.get(id)) {
+            votes.inFavorById.set(id);
+            if (++votes.inFavorCount == 1 + _numOfValidators / 2) {
+                _acceptClaim(application, r, epochHash);
+            }
+        }
+    }
+
+    /// @notice Get the number of validators.
+    function numOfValidators() external view returns (uint256) {
+        return _numOfValidators;
+    }
+
+    /// @notice Get the ID of a validator.
+    /// @param validator The validator address
+    /// @dev Validators have IDs greater than zero.
+    /// @dev Non-validators are assigned to ID zero.
+    function validatorId(address validator) external view returns (uint256) {
+        return _validatorId[validator];
+    }
+
+    /// @notice Get the address of a validator by its ID.
+    /// @param id The validator ID
+    /// @dev Validator IDs range from 1 to `N`, the total number of validators.
+    /// @dev Invalid IDs are assigned to the zero address.
+    function validatorById(uint256 id) external view returns (address) {
+        return _validatorById[id];
+    }
+
+    /// @notice Get the number of validators in favor of a claim.
+    /// @param application The application address
+    /// @param r The input range
+    /// @param epochHash The epoch hash
+    /// @return Number of validators in favor of claim.
+    function numOfValidatorsInFavorOf(
+        address application,
+        InputRange calldata r,
+        bytes32 epochHash
+    ) external view returns (uint256) {
+        return _getVotes(application, r, epochHash).inFavorCount;
+    }
+
+    /// @notice Check whether a validator is in favor of a claim.
+    /// @param application The application address
+    /// @param r The input range
+    /// @param epochHash The epoch hash
+    /// @param id The ID of the validator
+    /// @return Whether validator is in favor of claim
+    /// @dev Assumes the provided ID is valid
+    function isValidatorInFavorOf(
+        address application,
+        InputRange calldata r,
+        bytes32 epochHash,
+        uint256 id
+    ) external view returns (bool) {
+        return _getVotes(application, r, epochHash).inFavorById.get(id);
+    }
+
+    /// @notice Get a `Votes` structure from storage from a given claim.
+    /// @param application The application address
+    /// @param r The input range
+    /// @param epochHash The epoch hash
+    /// @return The `Votes` structure related to given claim
+    function _getVotes(
+        address application,
+        InputRange calldata r,
+        bytes32 epochHash
+    ) internal view returns (Votes storage) {
+        return _votes[application][r.firstIndex][r.lastIndex][epochHash];
+    }
+}