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| pragma solidity ^0.5.8; | ||
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| // From https://github.com/OpenZeppelin/openzeppelin-contracts/blob/master/contracts/math/Math.sol | ||
| // Subject to the MIT license. | ||
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| /** | ||
| * @dev 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 this library instead of the unchecked operations eliminates an entire | ||
| * class of bugs, so it's recommended to use it always. | ||
| */ | ||
| library SafeMath { | ||
| /** | ||
| * @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) { | ||
| uint256 c = a + b; | ||
| require(c >= a, "SafeMath: addition overflow"); | ||
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| return c; | ||
| } | ||
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| /** | ||
| * @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 sub(a, b, "SafeMath: subtraction overflow"); | ||
| } | ||
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| /** | ||
| * @dev Returns the subtraction of two unsigned integers, reverting with custom message on | ||
| * overflow (when the result is negative). | ||
| * | ||
| * Counterpart to Solidity's `-` operator. | ||
| * | ||
| * Requirements: | ||
| * - Subtraction cannot overflow. | ||
| * | ||
| * NOTE: This is a feature of the next version of OpenZeppelin Contracts. | ||
| * @dev Get it via `npm install @openzeppelin/contracts@next`. | ||
| */ | ||
| function sub(uint256 a, uint256 b, string memory errorMessage) internal pure returns (uint256) { | ||
| require(b <= a, errorMessage); | ||
| uint256 c = a - b; | ||
|
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| return c; | ||
| } | ||
|
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| /** | ||
| * @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) { | ||
| // 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 0; | ||
| } | ||
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| uint256 c = a * b; | ||
| require(c / a == b, "SafeMath: multiplication overflow"); | ||
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| return c; | ||
| } | ||
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| /** | ||
| * @dev Returns the integer division of two unsigned integers. Reverts 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) internal pure returns (uint256) { | ||
| return div(a, b, "SafeMath: division by zero"); | ||
| } | ||
|
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| /** | ||
| * @dev Returns the integer division of two unsigned integers. Reverts 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. | ||
| * NOTE: This is a feature of the next version of OpenZeppelin Contracts. | ||
| * @dev Get it via `npm install @openzeppelin/contracts@next`. | ||
| */ | ||
| function div(uint256 a, uint256 b, string memory errorMessage) internal pure returns (uint256) { | ||
| // Solidity only automatically asserts when dividing by 0 | ||
| require(b > 0, errorMessage); | ||
| uint256 c = a / b; | ||
| // assert(a == b * c + a % b); // There is no case in which this doesn't hold | ||
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| return c; | ||
| } | ||
|
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| /** | ||
| * @dev Returns the remainder of dividing two unsigned integers. (unsigned integer modulo), | ||
| * Reverts 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 mod(a, b, "SafeMath: modulo by zero"); | ||
| } | ||
|
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| /** | ||
| * @dev Returns the remainder of dividing two unsigned integers. (unsigned integer modulo), | ||
| * Reverts with custom message 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. | ||
| * | ||
| * NOTE: This is a feature of the next version of OpenZeppelin Contracts. | ||
| * @dev Get it via `npm install @openzeppelin/contracts@next`. | ||
| */ | ||
| function mod(uint256 a, uint256 b, string memory errorMessage) internal pure returns (uint256) { | ||
| require(b != 0, errorMessage); | ||
| return a % b; | ||
| } | ||
| } |
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