update math

contracts/MultiplierPointMath.sol

@@ -1,51 +1,135 @@
 // SPDX-License-Identifier: MIT-1.0
-pragma solidity ^0.8.18;
+pragma solidity ^0.8.26;
 
 import { Math } from "@openzeppelin/contracts/utils/math/Math.sol";
 
 abstract contract MultiplierPointMath {
-    uint256 public constant YEAR = 365 days;
-    uint256 public constant MP_APY = 1;
+    /// @notice One (mean) tropical year, in seconds.
+    uint256 public constant YEAR = 365 days + 5 hours + 48 minutes + 45 seconds;
+    /// @notice Multiplier points annual percentage yield.
+    uint256 public constant MP_APY = 100;
+    /// @notice Accrued multiplier points maximum multiplier.
     uint256 public constant MAX_MULTIPLIER = 4;
+    /// @notice The accrue rate period of time over which multiplier points are calculated.
+    uint256 public constant ACCURE_RATE = 1 weeks;
+    /// @notice Minimal value to generate 1 multiplier point in the accrue rate period (rounded up).
+    uint256 public constant MIN_BALANCE = (((YEAR * 100) - 1) / (MP_APY * ACCURE_RATE)) + 1;
+    /// @notice Multiplier points absolute maximum multiplier
+    uint256 public constant MAX_MULTIPLIER_ABSOLUTE = 1 + (2 * (MAX_MULTIPLIER * MP_APY) / 100);
+    /// @notice Maximum lockup period
+    uint256 public constant MAX_LOCKUP_PERIOD = MAX_MULTIPLIER * YEAR;
 
     /**
-     * @notice Calculates multiplier points accurred for given `_amount` and  `_seconds` time passed
-     * @param _amount quantity of tokens
-     * @param _seconds time in seconds
+     * @notice Calculates the accrued multiplier points (MPs) over a time period Δt, based on the account balance
+     * @param _balance Represents the current account balance
+     * @param _deltaTime The time difference or the duration over which the multiplier points are accrued, expressed in
+     * seconds
      * @return _accuredMP points accured for given `_amount` and  `_seconds`
+     * 51584438
+     * 10000000
      */
-    function _calculateAccuredMP(uint256 _amount, uint256 _seconds) internal pure returns (uint256 _accuredMP) {
-        return Math.mulDiv(_amount, _seconds, YEAR) * MP_APY;
+    function _calculateAccuredMP(uint256 _balance, uint256 _deltaTime) public pure returns (uint256 _accuredMP) {
+        return Math.mulDiv(_balance, _deltaTime * MP_APY, YEAR * 100);
     }
 
     /**
-     * @notice Calculates bonus multiplier points for given `_amount` and `_lockedSeconds`
+     * @notice Calculates the bonus multiplier points (MPs) earned when a balance Δa is locked for a specified duration
+     * t_lock.
+     * It is equivalent to the accrued multiplier points function but specifically applied in the context of a locked
+     * balance.
      * @param _amount quantity of tokens
      * @param _lockedSeconds time in seconds locked
      * @return _bonusMP bonus multiplier points for given `_amount` and `_lockedSeconds`
      */
-    function _calculateBonusMP(uint256 _amount, uint256 _lockedSeconds) internal pure returns (uint256 _bonusMP) {
-        _bonusMP = _amount;
-        if (_lockedSeconds > 0) {
-            _bonusMP += _calculateAccuredMP(_amount, _lockedSeconds);
-        }
+    function _calculateBonusMP(uint256 _amount, uint256 _lockedSeconds) public pure returns (uint256 _bonusMP) {
+        return _calculateAccuredMP(_amount, _lockedSeconds);
+    }
+
+    /**
+     * @notice Calculates the initial multiplier points (MPs) based on the balance change Δa. The result is equal to
+     * the amount of balance added.
+     * @param _amount Represents the change in balance.
+     */
+    function _calculateInitialMP(uint256 _amount) public pure returns (uint256 _initialMP) {
+        return _amount;
     }
 
     /**
-     * @notice Calculates minimum stake to genarate 1 multiplier points for given `_seconds`
-     * @param _seconds time in seconds
-     * @return _minimumStake minimum quantity of tokens
+     * @notice Calculates the reduction in multiplier points (MPs) when a portion of the balance Δa `_reducedAmount` is
+     * removed from the total balance a_bal `_currentBalance`.
+     * The reduction is proportional to the ratio of the removed balance to the total balance, applied to the current
+     * multiplier points $mp$.
+     * @param _mp Represents the current multiplier points
+     * @param _currentBalance The total account balance before the removal of Δa `_reducedBalance`
+     * @param _reducedAmount reduced balance
+     * @return _reducedMP Multiplier points to reduce from `_mp`
      */
-    function _calculateMinimumStake(uint256 _seconds) internal pure returns (uint256 _minimumStake) {
-        return YEAR / (_seconds * MP_APY);
+    function _calculateReducedMP(
+        uint256 _mp,
+        uint256 _currentBalance,
+        uint256 _reducedAmount
+    )
+        public
+        pure
+        returns (uint256 _reducedMP)
+    {
+        return Math.mulDiv(_mp, _currentBalance, _reducedAmount);
     }
 
     /**
      * @notice Calculates maximum stake a given `_amount` can be generated with `MAX_MULTIPLIER`
-     * @param _amount quantity of tokens
+     * @param _balance quantity of tokens
      * @return _maxMPAccured maximum quantity of muliplier points that can be generated for given `_amount`
      */
-    function _calculateMaxAccuredMP(uint256 _amount) internal pure returns (uint256 _maxMPAccured) {
-        return _calculateAccuredMP(_amount, MAX_MULTIPLIER * YEAR);
+    function _calculateMaxAccuredMP(uint256 _balance) public pure returns (uint256 _maxMPAccured) {
+        return Math.mulDiv(_balance, MAX_MULTIPLIER * MP_APY, 100);
+    }
+
+    /**
+     * @notice The maximum total multiplier points that can be generated for a determined amount of balance and lock
+     * duration.
+     * @param _balance Represents the current account balance
+     * @param _lockTime The time duration for which the balance is locked
+     * @return _maxMP Maximum multiplier points that can be generated for given `_balance` and `_lockTime`
+     */
+    function _calculateMaxMP(uint256 _balance, uint256 _lockTime) public pure returns (uint256 _maxMP) {
+        return _balance + Math.mulDiv(_balance * MP_APY, (MAX_MULTIPLIER * YEAR) + _lockTime, YEAR * 100);
+    }
+
+    /**
+     * @dev Caution: This value is estimated and can be incorrect due precision loss.
+     * @notice Estimates the time an account set as locked time.
+     * @param _mpMax Maximum multiplier points calculated from the current balance.
+     * @param _currentBalance Current balance used to calculate the maximum multiplier points.
+     */
+    function _estimateLockTime(uint256 _mpMax, uint256 _currentBalance) public pure returns (uint256 _lockTime) {
+        return Math.mulDiv((_mpMax - _currentBalance) * 100, YEAR, _currentBalance * MP_APY, Math.Rounding.Ceil)
+            - MAX_LOCKUP_PERIOD;
+    }
+
+    /**
+     * @dev Caution: This value is estimated and can be incorrect due precision loss.
+     * @notice Calculates the remaining lock time available for a given `_mpMax` and `_currentBalance`
+     * @param _mpMax Maximum multiplier points calculated from the current balance.
+     * @param _currentBalance Current balance used to calculate the maximum multiplier points.
+     */
+    function _remainingLockTimeAvailable(
+        uint256 _mpMax,
+        uint256 _currentBalance
+    )
+        public
+        pure
+        returns (uint256 _lockTime)
+    {
+        return Math.mulDiv((_currentBalance * MAX_MULTIPLIER_ABSOLUTE) - _mpMax, YEAR, _currentBalance);
+    }
+
+    /**
+     * @notice Calculates the lock time for a given bonus multiplier points and current balance.
+     * @param _bonusMP bonus multiplier points intended to be generated
+     * @param _currentBalance current balance
+     */
+    function _calculateLockTime(uint256 _bonusMP, uint256 _currentBalance) public pure returns (uint256 _lockTime) {
+        return Math.mulDiv(_bonusMP * 100, YEAR, _currentBalance * MP_APY);
     }
 }

contracts/StakeMath.sol

@@ -0,0 +1,153 @@
+// SPDX-License-Identifier: MIT-1.0
+pragma solidity ^0.8.26;
+
+import { Math } from "@openzeppelin/contracts/utils/math/Math.sol";
+import { MultiplierPointMath } from "./MultiplierPointMath.sol";
+
+abstract contract StakeMath is MultiplierPointMath {
+    /// @notice Minimal lockup time
+    uint256 public constant MIN_LOCKUP_TIME = 1 weeks;
+
+    /**
+     * @notice Calculates the bonus multiplier points earned when a balance Δa is increased an optionally locked for a
+     * specified duration
+     * @param _balance Account current balance
+     * @param _maxMP Account current max multiplier points
+     * @param _lockEndTime Account current lock end timestamp
+     * @param _processTime Process current timestamp
+     * @param _increasedAmount Increased amount of balance
+     * @param _increasedLockSeconds Increased amount of seconds to lock
+     * @return _deltaMpTotal Increased amount of total multiplier points
+     * @return _newMaxMP Account new max multiplier points
+     * @return _newLockEnd Account new lock end timestamp
+     */
+    function _calculateStake(
+        uint256 _balance,
+        uint256 _maxMP,
+        uint256 _lockEndTime,
+        uint256 _processTime,
+        uint256 _increasedAmount,
+        uint256 _increasedLockSeconds
+    )
+        public
+        pure
+        returns (uint256 _deltaMpTotal, uint256 _newMaxMP, uint256 _newLockEnd)
+    {
+        uint256 newBalance = _balance + _increasedAmount;
+        require(newBalance >= MIN_BALANCE, "StakeMath: balance too low");
+        _newLockEnd = Math.max(_lockEndTime, _processTime) + _increasedLockSeconds;
+        uint256 dt_lock = _newLockEnd - _processTime;
+        require(dt_lock == 0 || dt_lock >= MIN_LOCKUP_TIME, "StakeMath: lockup time too low");
+        require(dt_lock <= MAX_LOCKUP_PERIOD, "StakeMath: lockup time too high");
+
+        uint256 deltaMpBonus;
+        if (dt_lock > 0) {
+            deltaMpBonus = _calculateBonusMP(_increasedAmount, dt_lock);
+        }
+
+        if (_balance > 0 && _increasedLockSeconds > 0) {
+            deltaMpBonus += _calculateBonusMP(_balance, _increasedLockSeconds);
+        }
+
+        _deltaMpTotal = _calculateInitialMP(_increasedAmount) + deltaMpBonus;
+        _newMaxMP = _maxMP + _deltaMpTotal + _calculateAccuredMP(_balance, MAX_MULTIPLIER * YEAR);
+
+        require(
+            _newMaxMP <= MAX_MULTIPLIER_ABSOLUTE * (_balance + _increasedAmount), "StakeMath: max multiplier exceeded"
+        );
+    }
+
+    /**
+     * @notice Calculates the bonus multiplier points earned when a balance Δa is locked for a specified duration
+     * @param _balance Account current balance
+     * @param _maxMP Account current max multiplier points
+     * @param _lockEndTime Account current lock end timestamp
+     * @param _processTime Process current timestamp
+     * @param _increasedLockSeconds Increased amount of seconds to lock
+     * @return _deltaMpTotal Increased amount of total multiplier points
+     * @return _newMaxMP Account new max multiplier points
+     * @return _newLockEnd Account new lock end timestamp
+     */
+    function calculateLock(
+        uint256 _balance,
+        uint256 _maxMP,
+        uint256 _lockEndTime,
+        uint256 _processTime,
+        uint256 _increasedLockSeconds
+    )
+        public
+        pure
+        returns (uint256 _deltaMpTotal, uint256 _newMaxMP, uint256 _newLockEnd)
+    {
+        require(_balance > 0);
+        require(_increasedLockSeconds > 0);
+
+        _newLockEnd = Math.max(_lockEndTime, _processTime) + _increasedLockSeconds;
+        uint256 dt_lock = _newLockEnd - _processTime;
+        require(dt_lock == 0 || dt_lock >= MIN_LOCKUP_TIME, "StakeMath: lockup time too low");
+        require(dt_lock <= MAX_LOCKUP_PERIOD, "StakeMath: lockup time too high");
+
+        _deltaMpTotal += _calculateBonusMP(_balance, _increasedLockSeconds);
+        _newMaxMP = _maxMP + _deltaMpTotal;
+
+        require(_newMaxMP <= MAX_MULTIPLIER_ABSOLUTE * (_balance), "StakeMath: max multiplier exceeded");
+    }
+
+    /**
+     *
+     * @param _balance Account current balance
+     * @param _lockEndTime Account current lock end timestamp
+     * @param _processTime Process current timestamp
+     * @param _totalMP Account current total multiplier points
+     * @param _maxMP Account current max multiplier points
+     * @param _reducedAmount Reduced amount of balance
+     * @return _deltaMpTotal Increased amount of total multiplier points
+     * @return _deltaMpMax Increased amount of max multiplier points
+     */
+    function _calculateUnstake(
+        uint256 _balance,
+        uint256 _lockEndTime,
+        uint256 _processTime,
+        uint256 _totalMP,
+        uint256 _maxMP,
+        uint256 _reducedAmount
+    )
+        public
+        pure
+        returns (uint256 _deltaMpTotal, uint256 _deltaMpMax)
+    {
+        require(_lockEndTime <= _processTime, "StakeMath: lockup not ended");
+        require(_balance >= _reducedAmount, "StakeMath: balance too low");
+        uint256 newBalance = _balance - _reducedAmount;
+        require(newBalance == 0 || newBalance >= MIN_BALANCE, "StakeMath: balance too low");
+        _deltaMpTotal = _calculateReducedMP(_totalMP, _balance, _reducedAmount);
+        _deltaMpMax = _calculateReducedMP(_maxMP, _balance, _reducedAmount);
+    }
+
+    /**
+     * @notice Calculates the accrued multiplier points for a given balance and seconds passed since last accrual
+     * @param _balance Account current balance
+     * @param _totalMP Account current total multiplier points
+     * @param _maxMP Account current max multiplier points
+     * @param _lastAccrualTime Account current last accrual timestamp
+     * @param _processTime Process current timestamp
+     * @return _deltaMpTotal Increased amount of total multiplier points
+     */
+    function _calculateAccrual(
+        uint256 _balance,
+        uint256 _totalMP,
+        uint256 _maxMP,
+        uint256 _lastAccrualTime,
+        uint256 _processTime
+    )
+        public
+        pure
+        returns (uint256 _deltaMpTotal)
+    {
+        uint256 dt = _processTime - _lastAccrualTime;
+        require(dt >= ACCURE_RATE, "StakeMath: no enough time passed");
+        if (_totalMP <= _maxMP) {
+            _deltaMpTotal = Math.min(_calculateAccuredMP(_balance, dt), _maxMP - _totalMP);
+        }
+    }
+}