// Brought from https://github.com/aragon/aragonOS/blob/v4.3.0/contracts/lib/math/SafeMath.sol
// Adapted to use pragma ^0.5.8 and satisfy our linter rules

pragma solidity >=0.4.24 <0.6.0;


/**
 * @title SafeMath
 * @dev Math operations with safety checks that revert on error
 */
library SafeMath {
    string private constant ERROR_ADD_OVERFLOW = "MATH_ADD_OVERFLOW";
    string private constant ERROR_SUB_UNDERFLOW = "MATH_SUB_UNDERFLOW";
    string private constant ERROR_MUL_OVERFLOW = "MATH_MUL_OVERFLOW";
    string private constant ERROR_DIV_ZERO = "MATH_DIV_ZERO";

    /**
    * @dev Multiplies two numbers, reverts on overflow.
    */
    function mul(uint256 _a, uint256 _b) internal pure returns (uint256) {
        // Gas optimization: this is cheaper than requiring 'a' not being 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, ERROR_MUL_OVERFLOW);

        return c;
    }

    /**
    * @dev Integer division of two numbers truncating the quotient, reverts on division by zero.
    */
    function div(uint256 _a, uint256 _b) internal pure returns (uint256) {
        require(_b > 0, ERROR_DIV_ZERO); // Solidity only automatically asserts when dividing by 0
        uint256 c = _a / _b;
        // assert(_a == _b * c + _a % _b); // There is no case in which this doesn't hold

        return c;
    }

    /**
    * @dev Subtracts two numbers, reverts on overflow (i.e. if subtrahend is greater than minuend).
    */
    function sub(uint256 _a, uint256 _b) internal pure returns (uint256) {
        require(_b <= _a, ERROR_SUB_UNDERFLOW);
        uint256 c = _a - _b;

        return c;
    }

    /**
    * @dev Adds two numbers, reverts on overflow.
    */
    function add(uint256 _a, uint256 _b) internal pure returns (uint256) {
        uint256 c = _a + _b;
        require(c >= _a, ERROR_ADD_OVERFLOW);

        return c;
    }

    /**
    * @dev Divides two numbers and returns the remainder (unsigned integer modulo),
    * reverts when dividing by zero.
    */
    function mod(uint256 a, uint256 b) internal pure returns (uint256) {
        require(b != 0, ERROR_DIV_ZERO);
        return a % b;
    }
}