[ERC2917] ステーキング報酬をオンチェーンで計算する仕組みを理解しよう！

Reward_U = Σ (Δp_i / ΔP_i) × ΔG_i

interface IERC2917 is IERC20 {

    /// @dev This emit when interests amount per block is changed by the owner of the contract.
    /// It emits with the old interests amount and the new interests amount.
    event InterestRatePerBlockChanged (uint oldValue, uint newValue);

    /// @dev This emit when a users' productivity has changed
    /// It emits with the user's address and the value after the change.
    event ProductivityIncreased (address indexed user, uint value);

    /// @dev This emit when a users' productivity has changed
    /// It emits with the user's address and the value after the change.
    event ProductivityDecreased (address indexed user, uint value);

    
    /// @dev Return the current contract's interests rate per block.
    /// @return The amount of interests currently producing per each block.
    function interestsPerBlock() external view returns (uint);

    /// @notice Change the current contract's interests rate.
    /// @dev Note the best practice will be restrict the gross product provider's contract address to call this.
    /// @return The true/false to notice that the value has successfully changed or not, when it succeed, it will emite the InterestRatePerBlockChanged event.
    function changeInterestRatePerBlock(uint value) external returns (bool);

    /// @notice It will get the productivity of given user.
    /// @dev it will return 0 if user has no productivity proved in the contract.
    /// @return user's productivity and overall productivity.
    function getProductivity(address user) external view returns (uint, uint);

    /// @notice increase a user's productivity.
    /// @dev Note the best practice will be restrict the callee to prove of productivity's contract address.
    /// @return true to confirm that the productivity added success.
    function increaseProductivity(address user, uint value) external returns (bool);

    /// @notice decrease a user's productivity.
    /// @dev Note the best practice will be restrict the callee to prove of productivity's contract address.
    /// @return true to confirm that the productivity removed success.
    function decreaseProductivity(address user, uint value) external returns (bool);

    /// @notice take() will return the interests that callee will get at current block height.
    /// @dev it will always calculated by block.number, so it will change when block height changes.
    /// @return amount of the interests that user are able to mint() at current block height.
    function take() external view returns (uint);

    /// @notice similar to take(), but with the block height joined to calculate return.
    /// @dev for instance, it returns (_amount, _block), which means at block height _block, the callee has accumulated _amount of interests.
    /// @return amount of interests and the block height.
    function takeWithBlock() external view returns (uint, uint);

    /// @notice mint the available interests to callee.
    /// @dev once it mint, the amount of interests will transfer to callee's address.
    /// @return the amount of interests minted.
    function mint() external returns (uint);
}

event InterestRatePerBlockChanged (uint oldValue, uint newValue);

event ProductivityIncreased (address indexed user, uint value);

event ProductivityDecreased (address indexed user, uint value);

function interestsPerBlock() external view returns (uint);

function changeInterestRatePerBlock(uint value) external returns (bool);

function getProductivity(address user) external view returns (uint, uint);

function increaseProductivity(address user, uint value) external returns (bool);

function decreaseProductivity(address user, uint value) external returns (bool);

function take() external view returns (uint);

function takeWithBlock() external view returns (uint, uint);

function mint() external returns (uint);