// SPDX-License-Identifier: LGPL-3.0-only
pragma solidity >=0.7.0 <0.9.0;

/**
 * @title SafeMath
 * @notice Math operations with safety checks that revert on error (overflow/underflow)
 */
library SafeMath {
    /**
     * @notice Multiplies two numbers, reverts on overflow.
     * @param a First number
     * @param b Second number
     * @return Product of a and b
     */
    function mul(uint256 a, uint256 b) internal pure returns (uint256) {
        // Gas optimization: this is cheaper than requiring 'a' not to be zero, but the
        // benefit is lost if 'b' is also tested.
        // See: https://github.com/OpenZeppelin/openzeppelin-solidity/pull/522
        if (a == 0) {
            return 0;
        }

        uint256 c = a * b;
        require(c / a == b);

        return c;
    }

    /**
     * @notice Subtracts two numbers, reverts on overflow (i.e. if subtrahend is greater than minuend).
     * @param a First number
     * @param b Second number
     * @return Difference of a and b
     */
    function sub(uint256 a, uint256 b) internal pure returns (uint256) {
        require(b <= a);
        uint256 c = a - b;

        return c;
    }

    /**
     * @notice Adds two numbers, reverts on overflow.
     * @param a First number
     * @param b Second number
     * @return Sum of a and b
     */
    function add(uint256 a, uint256 b) internal pure returns (uint256) {
        uint256 c = a + b;
        require(c >= a);

        return c;
    }

    /**
     * @notice Returns the largest of two numbers.
     * @param a First number
     * @param b Second number
     * @return Largest of a and b
     */
    function max(uint256 a, uint256 b) internal pure returns (uint256) {
        return a >= b ? a : b;
    }
}