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// SPDX-License-Identifier: MIT
// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts v4.4.1 (utils/math/SafeMath.sol)
// OpenZeppelin Contracts (last updated v4.9.0) (utils/math/SafeMath.sol)
pragma solidity ^0.8.0;
pragma solidity ^0.8.0;
// CAUTION
// CAUTION
// This version of SafeMath should only be used with Solidity 0.8 or later,
// 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.
// because it relies on the compiler's built in overflow checks.
/**
/**
* @dev Wrappers over Solidity's arithmetic operations.
* @dev Wrappers over Solidity's arithmetic operations.
*
*
* NOTE: `SafeMath` is generally not needed starting with Solidity 0.8, since the compiler
* NOTE: `SafeMath` is generally not needed starting with Solidity 0.8, since the compiler
* now has built in overflow checking.
* now has built in overflow checking.
*/
*/
library SafeMath {
library SafeMath {
/**
/**
* @dev Returns the addition of two unsigned integers, with an overflow flag.
* @dev Returns the addition of two unsigned integers, with an overflow flag.
*
*
* _Available since v3.4._
* _Available since v3.4._
*/
*/
function tryAdd(uint256 a, uint256 b) internal pure returns (bool, uint256) {
function tryAdd(uint256 a, uint256 b) internal pure returns (bool, uint256) {
unchecked {
unchecked {
uint256 c = a + b;
uint256 c = a + b;
if (c < a) return (false, 0);
if (c < a) return (false, 0);
return (true, c);
return (true, c);
}
}
}
}
/**
/**
* @dev Returns the substraction of two unsigned integers, with an overflow flag.
* @dev Returns the subtraction of two unsigned integers, with an overflow flag.
*
*
* _Available since v3.4._
* _Available since v3.4._
*/
*/
function trySub(uint256 a, uint256 b) internal pure returns (bool, uint256) {
function trySub(uint256 a, uint256 b) internal pure returns (bool, uint256) {
unchecked {
unchecked {
if (b > a) return (false, 0);
if (b > a) return (false, 0);
return (true, a - b);
return (true, a - b);
}
}
}
}
/**
/**
* @dev Returns the multiplication of two unsigned integers, with an overflow flag.
* @dev Returns the multiplication of two unsigned integers, with an overflow flag.
*
*
* _Available since v3.4._
* _Available since v3.4._
*/
*/
function tryMul(uint256 a, uint256 b) internal pure returns (bool, uint256) {
function tryMul(uint256 a, uint256 b) internal pure returns (bool, uint256) {
unchecked {
unchecked {
// Gas optimization: this is cheaper than requiring 'a' not being zero, but the
// Gas optimization: this is cheaper than requiring 'a' not being zero, but the
// benefit is lost if 'b' is also tested.
// benefit is lost if 'b' is also tested.
// See: https://github.com/OpenZeppelin/openzeppelin-contracts/pull/522
// See: https://github.com/OpenZeppelin/openzeppelin-contracts/pull/522
if (a == 0) return (true, 0);
if (a == 0) return (true, 0);
uint256 c = a * b;
uint256 c = a * b;
if (c / a != b) return (false, 0);
if (c / a != b) return (false, 0);
return (true, c);
return (true, c);
}
}
}
}
/**
/**
* @dev Returns the division of two unsigned integers, with a division by zero flag.
* @dev Returns the division of two unsigned integers, with a division by zero flag.
*
*
* _Available since v3.4._
* _Available since v3.4._
*/
*/
function tryDiv(uint256 a, uint256 b) internal pure returns (bool, uint256) {
function tryDiv(uint256 a, uint256 b) internal pure returns (bool, uint256) {
unchecked {
unchecked {
if (b == 0) return (false, 0);
if (b == 0) return (false, 0);
return (true, a / b);
return (true, a / b);
}
}
}
}
/**
/**
* @dev Returns the remainder of dividing two unsigned integers, with a division by zero flag.
* @dev Returns the remainder of dividing two unsigned integers, with a division by zero flag.
*
*
* _Available since v3.4._
* _Available since v3.4._
*/
*/
function tryMod(uint256 a, uint256 b) internal pure returns (bool, uint256) {
function tryMod(uint256 a, uint256 b) internal pure returns (bool, uint256) {
unchecked {
unchecked {
if (b == 0) return (false, 0);
if (b == 0) return (false, 0);
return (true, a % b);
return (true, a % b);
}
}
}
}
/**
/**
* @dev Returns the addition of two unsigned integers, reverting on
* @dev Returns the addition of two unsigned integers, reverting on
* overflow.
* overflow.
*
*
* Counterpart to Solidity's `+` operator.
* Counterpart to Solidity's `+` operator.
*
*
* Requirements:
* Requirements:
*
*
* - Addition cannot overflow.
* - Addition cannot overflow.
*/
*/
function add(uint256 a, uint256 b) internal pure returns (uint256) {
function add(uint256 a, uint256 b) internal pure returns (uint256) {
return a + b;
return a + b;
}
}
/**
/**
* @dev Returns the subtraction of two unsigned integers, reverting on
* @dev Returns the subtraction of two unsigned integers, reverting on
* overflow (when the result is negative).
* overflow (when the result is negative).
*
*
* Counterpart to Solidity's `-` operator.
* Counterpart to Solidity's `-` operator.
*
*
* Requirements:
* Requirements:
*
*
* - Subtraction cannot overflow.
* - Subtraction cannot overflow.
*/
*/
function sub(uint256 a, uint256 b) internal pure returns (uint256) {
function sub(uint256 a, uint256 b) internal pure returns (uint256) {
return a - b;
return a - b;
}
}
/**
/**
* @dev Returns the multiplication of two unsigned integers, reverting on
* @dev Returns the multiplication of two unsigned integers, reverting on
* overflow.
* overflow.
*
*
* Counterpart to Solidity's `*` operator.
* Counterpart to Solidity's `*` operator.
*
*
* Requirements:
* Requirements:
*
*
* - Multiplication cannot overflow.
* - Multiplication cannot overflow.
*/
*/
function mul(uint256 a, uint256 b) internal pure returns (uint256) {
function mul(uint256 a, uint256 b) internal pure returns (uint256) {
return a * b;
return a * b;
}
}
/**
/**
* @dev Returns the integer division of two unsigned integers, reverting on
* @dev Returns the integer division of two unsigned integers, reverting on
* division by zero. The result is rounded towards zero.
* division by zero. The result is rounded towards zero.
*
*
* Counterpart to Solidity's `/` operator.
* Counterpart to Solidity's `/` operator.
*
*
* Requirements:
* Requirements:
*
*
* - The divisor cannot be zero.
* - The divisor cannot be zero.
*/
*/
function div(uint256 a, uint256 b) internal pure returns (uint256) {
function div(uint256 a, uint256 b) internal pure returns (uint256) {
return a / b;
return a / b;
}
}
/**
/**
* @dev Returns the remainder of dividing two unsigned integers. (unsigned integer modulo),
* @dev Returns the remainder of dividing two unsigned integers. (unsigned integer modulo),
* reverting when dividing by zero.
* reverting when dividing by zero.
*
*
* Counterpart to Solidity's `%` operator. This function uses a `revert`
* Counterpart to Solidity's `%` operator. This function uses a `revert`
* opcode (which leaves remaining gas untouched) while Solidity uses an
* opcode (which leaves remaining gas untouched) while Solidity uses an
* invalid opcode to revert (consuming all remaining gas).
* invalid opcode to revert (consuming all remaining gas).
*
*
* Requirements:
* Requirements:
*
*
* - The divisor cannot be zero.
* - The divisor cannot be zero.
*/
*/
function mod(uint256 a, uint256 b) internal pure returns (uint256) {
function mod(uint256 a, uint256 b) internal pure returns (uint256) {
return a % b;
return a % b;
}
}
/**
/**
* @dev Returns the subtraction of two unsigned integers, reverting with custom message on
* @dev Returns the subtraction of two unsigned integers, reverting with custom message on
* overflow (when the result is negative).
* overflow (when the result is negative).
*
*
* CAUTION: This function is deprecated because it requires allocating memory for the error
* CAUTION: This function is deprecated because it requires allocating memory for the error
* message unnecessarily. For custom revert reasons use {trySub}.
* message unnecessarily. For custom revert reasons use {trySub}.
*
*
* Counterpart to Solidity's `-` operator.
* Counterpart to Solidity's `-` operator.
*
*
* Requirements:
* Requirements:
*
*
* - Subtraction cannot overflow.
* - Subtraction cannot overflow.
*/
*/
function sub(
function sub(uint256 a, uint256 b, string memory errorMessage) internal pure returns (uint256) {
uint256 a,
uint256 b,
string memory errorMessage
) internal pure returns (uint256) {
unchecked {
unchecked {
require(b <= a, errorMessage);
require(b <= a, errorMessage);
return a - b;
return a - b;
}
}
}
}
/**
/**
* @dev Returns the integer division of two unsigned integers, reverting with custom message on
* @dev Returns the integer division of two unsigned integers, reverting with custom message on
* division by zero. The result is rounded towards zero.
* division by zero. The result is rounded towards zero.
*
*
* Counterpart to Solidity's `/` operator. Note: this function uses a
* Counterpart to Solidity's `/` operator. Note: this function uses a
* `revert` opcode (which leaves remaining gas untouched) while Solidity
* `revert` opcode (which leaves remaining gas untouched) while Solidity
* uses an invalid opcode to revert (consuming all remaining gas).
* uses an invalid opcode to revert (consuming all remaining gas).
*
*
* Requirements:
* Requirements:
*
*
* - The divisor cannot be zero.
* - The divisor cannot be zero.
*/
*/
function div(
function div(uint256 a, uint256 b, string memory errorMessage) internal pure returns (uint256) {
uint256 a,
uint256 b,
string memory errorMessage
) internal pure returns (uint256) {
unchecked {
unchecked {
require(b > 0, errorMessage);
require(b > 0, errorMessage);
return a / b;
return a / b;
}
}
}
}
/**
/**
* @dev Returns the remainder of dividing two unsigned integers. (unsigned integer modulo),
* @dev Returns the remainder of dividing two unsigned integers. (unsigned integer modulo),
* reverting with custom message when dividing by zero.
* reverting with custom message when dividing by zero.
*
*
* CAUTION: This function is deprecated because it requires allocating memory for the error
* CAUTION: This function is deprecated because it requires allocating memory for the error
* message unnecessarily. For custom revert reasons use {tryMod}.
* message unnecessarily. For custom revert reasons use {tryMod}.
*
*
* Counterpart to Solidity's `%` operator. This function uses a `revert`
* Counterpart to Solidity's `%` operator. This function uses a `revert`
* opcode (which leaves remaining gas untouched) while Solidity uses an
* opcode (which leaves remaining gas untouched) while Solidity uses an
* invalid opcode to revert (consuming all remaining gas).
* invalid opcode to revert (consuming all remaining gas).
*
*
* Requirements:
* Requirements:
*
*
* - The divisor cannot be zero.
* - The divisor cannot be zero.
*/
*/
function mod(
function mod(uint256 a, uint256 b, string memory errorMessage) internal pure returns (uint256) {
uint256 a,
uint256 b,
string memory errorMessage
) internal pure returns (uint256) {
unchecked {
unchecked {
require(b > 0, errorMessage);
require(b > 0, errorMessage);
return a % b;
return a % b;
}
}
}
}
}
}