墨客科普 | MOAC BlockChain SafeMath库

　　在编写智能合约的时候需要注意的一个主要的安全特性：防止溢出和下溢。为了防止这些情况，OpenZeppelin建立了一个叫做SafeMath的库(library)，默认情况下可以防止这些问题。

　　什么是溢出(overflow)

　　假设我们有一个uint8, 只能存储8 bit数据。这意味着我们能存储的最大数字就是二进制11111111(或者说十进制的2^8-1 =255).

　　来看看下面的代码。最后 number 将会是什么值

　　在这个例子中，我们导致了溢出---虽然我们加了1，但是number出乎意料地等于0了。

　　下溢(underflow)也类似，如果你从一个等于0的uint8减去1, 它将变成255 (因为uint是无符号的，其不能等于负数)。

　　分析 SafeMath源码

　　1.加法，仅限内部调用，返回 uint256

　　require(c>=a && c>=b); //验证结果： 两个正数相加，和一定大于每个加数

　　2.减法，仅限内部调用，返回 uint256

　　require(b <= a) 因为返回值需要是 正数，所以此处判断 b必须小于等于a

　　3.乘法，仅限内部调用，返回 uint256

　　uint256 c = a * b; 容易溢出，比如 a=2,b=2^255 乘积 2^256 刚好溢出。结果取后面的256位(全为0)，导致 c=0。

　　所以使用 (a == 0 || c / a == b)，验证结果的一致性。

　　4.除法，仅限内部调用，返回 uint256

　　require(b > 0), 确保被除数不能为0

　　require(a == b * c + a % b);防止溢出，验证结果的一致性

　　总结：

　　不要直接使用简单的 "+-*/" ，尽量使用 library SafeMath 中的函数，避免整数溢出的隐患。

　　附：完整源码

　　pragma solidity ^0.4.24;

　　library SafeMath {

　　/**

　　* @dev Returns the addition of two unsigned integers, reverting on

　　* overflow.

　　*

　　* Counterpart to Solidity's `+` operator.

　　*

　　* Requirements:

　　* - Addition cannot overflow.

　　*/

　　function safeAdd(uint256 a, uint256 b) internal pure returns (uint256) {

　　uint256 c = a + b;

　　require(c >= a, "SafeMath: addition overflow");

　　return c;

　　}

　　/**

　　* @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 safeSub(uint256 a, uint256 b) internal pure returns (uint256) {

　　return safeSub(a, b, "SafeMath: subtraction overflow");

　　}

　　/**

　　* @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 safeSub(uint256 a, uint256 b, string memory errorMessage) internal pure returns (uint256) {

　　require(b <= a, errorMessage);

　　uint256 c = a - b;

　　return c;

　　}

　　/**

　　* @dev Returns the multiplication of two unsigned integers, reverting on

　　* overflow.

　　*

　　* Counterpart to Solidity's `*` operator.

　　*

　　* Requirements:

　　* - Multiplication cannot overflow.

　　*/

　　function safeMul(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.

　　if (a == 0) {

　　return 0;

　　}

　　uint256 c = a * b;

　　require(c / a == b, "SafeMath: multiplication overflow");

　　return c;

　　}

　　/**

　　* @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 safeDiv(uint256 a, uint256 b) internal pure returns (uint256) {

　　return safeDiv(a, b, "SafeMath: division by zero");

　　}

　　/**

　　* @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 safeDiv(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;

　　return c;

　　}

　　/**

　　* @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 safeMod(uint256 a, uint256 b) internal pure returns (uint256) {

　　return safeMod(a, b, "SafeMath: modulo by zero");

　　}

　　/**

　　* @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 safeMod(uint256 a, uint256 b, string memory errorMessage) internal pure returns (uint256) {

　　require(b != 0, errorMessage);

　　return a % b;

　　}

　　}

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