// SPDX-License-Identifier: GPL-3.0-or-later
// This program is free software: you can redistribute it and/or modify
// it under the terms of the GNU General Public License as published by
// the Free Software Foundation, either version 3 of the License, or
// (at your option) any later version.

// This program is distributed in the hope that it will be useful,
// but WITHOUT ANY WARRANTY; without even the implied warranty of
// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
// GNU General Public License for more details.

// You should have received a copy of the GNU General Public License
// along with this program.  If not, see <http://www.gnu.org/licenses/>.

pragma solidity ^0.8.0;

/**
 * @title FixedPoint
 * @dev Math library to operate with fixed point values with 18 decimals
 */
library FixedPoint {
    // 1 in fixed point value: 18 decimal places
    uint256 internal constant ONE = 1e18;

    /**
     * @dev Multiplication overflow
     */
    error FixedPointMulOverflow(uint256 a, uint256 b);

    /**
     * @dev Division by zero
     */
    error FixedPointZeroDivision();

    /**
     * @dev Division internal error
     */
    error FixedPointDivInternal(uint256 a, uint256 aInflated);

    /**
     * @dev Multiplies two fixed point numbers rounding down
     */
    function mulDown(uint256 a, uint256 b) internal pure returns (uint256) {
        unchecked {
            uint256 product = a * b;
            if (a != 0 && product / a != b) revert FixedPointMulOverflow(a, b);
            return product / ONE;
        }
    }

    /**
     * @dev Multiplies two fixed point numbers rounding up
     */
    function mulUp(uint256 a, uint256 b) internal pure returns (uint256) {
        unchecked {
            uint256 product = a * b;
            if (a != 0 && product / a != b) revert FixedPointMulOverflow(a, b);
            return product == 0 ? 0 : (((product - 1) / ONE) + 1);
        }
    }

    /**
     * @dev Divides two fixed point numbers rounding down
     */
    function divDown(uint256 a, uint256 b) internal pure returns (uint256) {
        unchecked {
            if (b == 0) revert FixedPointZeroDivision();
            if (a == 0) return 0;
            uint256 aInflated = a * ONE;
            if (aInflated / a != ONE) revert FixedPointDivInternal(a, aInflated);
            return aInflated / b;
        }
    }

    /**
     * @dev Divides two fixed point numbers rounding up
     */
    function divUp(uint256 a, uint256 b) internal pure returns (uint256) {
        unchecked {
            if (b == 0) revert FixedPointZeroDivision();
            if (a == 0) return 0;
            uint256 aInflated = a * ONE;
            if (aInflated / a != ONE) revert FixedPointDivInternal(a, aInflated);
            return ((aInflated - 1) / b) + 1;
        }
    }
}