common libraries
Wrappers over Solidity’s arithmetic operations with added overflow checks.
Arithmetic operations in Solidity wrap on overflow. This can easily result in bugs, because programmers usually assume that an overflow raises an error, which is the standard behavior in high level programming languages. SafeMath restores this intuition by reverting the transaction when an operation overflows.
Using safeMath to safely run mathematical operations
// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts v4.4.1 (utils/math/SafeMath.sol)
pragma solidity ^0.8.0;
// CAUTION
// This version of SafeMath should only be used with Solidity 0.8 or later,
// because it relies on the compiler's built in overflow checks.
/**
* @dev Wrappers over Solidity's arithmetic operations.
*
* NOTE: `SafeMath` is generally not needed starting with Solidity 0.8, since the compiler
* now has built in overflow checking.
*/
library SafeMath {
/**
* @dev Returns the addition of two unsigned integers, with an overflow flag.
*
* _Available since v3.4._
*/
function tryAdd(uint256 a, uint256 b) internal pure returns (bool, uint256) {
unchecked {
uint256 c = a + b;
if (c < a) return (false, 0);
return (true, c);
}
}
/**
* @dev Returns the substraction of two unsigned integers, with an overflow flag.
*
* _Available since v3.4._
*/
function trySub(uint256 a, uint256 b) internal pure returns (bool, uint256) {
unchecked {
if (b > a) return (false, 0);
return (true, a - b);
}
}
/**
* @dev Returns the multiplication of two unsigned integers, with an overflow flag.
*
* _Available since v3.4._
*/
function tryMul(uint256 a, uint256 b) internal pure returns (bool, uint256) {
unchecked {
// 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-contracts/pull/522>
if (a == 0) return (true, 0);
uint256 c = a * b;
if (c / a != b) return (false, 0);
return (true, c);
}
}
/**
* @dev Returns the division of two unsigned integers, with a division by zero flag.
*
* _Available since v3.4._
*/
function tryDiv(uint256 a, uint256 b) internal pure returns (bool, uint256) {
unchecked {
if (b == 0) return (false, 0);
return (true, a / b);
}
}
/**
* @dev Returns the remainder of dividing two unsigned integers, with a division by zero flag.
*
* _Available since v3.4._
*/
function tryMod(uint256 a, uint256 b) internal pure returns (bool, uint256) {
unchecked {
if (b == 0) return (false, 0);
return (true, a % b);
}
}
/**
* @dev Returns the addition of two unsigned integers, reverting on
* overflow.
*
* Counterpart to Solidity's `+` operator.
*
* Requirements:
*
* - Addition cannot overflow.
*/
function add(uint256 a, uint256 b) internal pure returns (uint256) {
return a + b;
}
/**
* @dev Returns the subtraction of two unsigned integers, reverting on
* overflow (when the result is negative).
*
* Counterpart to Solidity's `-` operator.
*
* Requirements:
*
* - Subtraction cannot overflow.
*/
function sub(uint256 a, uint256 b) internal pure returns (uint256) {
return a - b;
}
/**
* @dev Returns the multiplication of two unsigned integers, reverting on
* overflow.
*
* Counterpart to Solidity's `*` operator.
*
* Requirements:
*
* - Multiplication cannot overflow.
*/
function mul(uint256 a, uint256 b) internal pure returns (uint256) {
return a * b;
}
/**
* @dev Returns the integer division of two unsigned integers, reverting on
* division by zero. The result is rounded towards zero.
*
* Counterpart to Solidity's `/` operator.
*
* Requirements:
*
* - The divisor cannot be zero.
*/
function div(uint256 a, uint256 b) internal pure returns (uint256) {
return a / b;
}
/**
* @dev Returns the remainder of dividing two unsigned integers. (unsigned integer modulo),
* reverting when dividing by zero.
*
* Counterpart to Solidity's `%` operator. This function uses a `revert`
* opcode (which leaves remaining gas untouched) while Solidity uses an
* invalid opcode to revert (consuming all remaining gas).
*
* Requirements:
*
* - The divisor cannot be zero.
*/
function mod(uint256 a, uint256 b) internal pure returns (uint256) {
return a % b;
}
/**
* @dev Returns the subtraction of two unsigned integers, reverting with custom message on
* overflow (when the result is negative).
*
* CAUTION: This function is deprecated because it requires allocating memory for the error
* message unnecessarily. For custom revert reasons use {trySub}.
*
* Counterpart to Solidity's `-` operator.
*
* Requirements:
*
* - Subtraction cannot overflow.
*/
function sub(
uint256 a,
uint256 b,
string memory errorMessage
) internal pure returns (uint256) {
unchecked {
require(b <= a, errorMessage);
return a - b;
}
}
/**
* @dev Returns the integer division of two unsigned integers, reverting with custom message on
* division by zero. The result is rounded towards zero.
*
* Counterpart to Solidity's `/` operator. Note: this function uses a
* `revert` opcode (which leaves remaining gas untouched) while Solidity
* uses an invalid opcode to revert (consuming all remaining gas).
*
* Requirements:
*
* - The divisor cannot be zero.
*/
function div(
uint256 a,
uint256 b,
string memory errorMessage
) internal pure returns (uint256) {
unchecked {
require(b > 0, errorMessage);
return a / b;
}
}
/**
* @dev Returns the remainder of dividing two unsigned integers. (unsigned integer modulo),
* reverting with custom message when dividing by zero.
*
* CAUTION: This function is deprecated because it requires allocating memory for the error
* message unnecessarily. For custom revert reasons use {tryMod}.
*
* Counterpart to Solidity's `%` operator. This function uses a `revert`
* opcode (which leaves remaining gas untouched) while Solidity uses an
* invalid opcode to revert (consuming all remaining gas).
*
* Requirements:
*
* - The divisor cannot be zero.
*/
function mod(
uint256 a,
uint256 b,
string memory errorMessage
) internal pure returns (uint256) {
unchecked {
require(b > 0, errorMessage);
return a % b;
}
}
}