Solidity的上溢與下溢

? ? Solidity是一種類似于JavaScript的語言，它面向物件，支持多繼承，可以一次回傳多個值，在開發智能合約的程序中，對應++、–這類操作要考慮變數的定義域，即要考慮變數的上溢與下溢問題，

• 資料上溢

uint8 numA = 255;
numA++;

? ? uint8的定義域為[0,255]，現在numA已經到頂了，numA++會使num變成0(由于256已經超過定義域，它會越過256，變成0)，即資料發生上溢(越過上邊界，叫上溢)，255 --> 256 -->0 上溢，

• 資料下溢

uint8 numB = 0;
numB--;

? ? numB本身是低水位線，現在numB-- 會使num變成255(由于-1已經超過定義域，所以它會越過-1，變成255)，即資料發生下溢(越過下邊界，叫下溢)，0–> -1 --> 255 下溢，

? ? 可以通過參考 OpenZeppelin的 SafeMath v2.5.x，或者自定義一個SafeMath合約，來避免該問題，
? ? 庫是 Solidity 中一種特殊的合約，它給原始資料型別增加了一些方法: add()， sub()， mul()， 以及 div()，
? ? 先參考或者import SafeMath庫，然后宣告 using SafeMath for uint256 ，再通過變數名來呼叫這些方法，

import "./safemath.sol";          //1)參考庫
using SafeMath for uint256;       //2)宣告指定的型別

uint256 a = 5;
uint256 b = a.add(3); // 5 + 3 = 8  //3)用變數名來呼叫方法
uint256 c = a.mul(2); // 5 * 2 = 10

1、庫合約

//safemath.sol

pragma solidity ^0.4.18;

/**
 * @title SafeMath
 * @dev Math operations with safety checks that throw on error
 */
library SafeMath {

  /**
  * @dev Multiplies two numbers, throws on overflow.
  */
  function mul(uint256 a, uint256 b) internal pure returns (uint256) {
    if (a == 0) {
      return 0;
    }
    uint256 c = a * b;
    assert(c / a == b);
    return c;
  }

  /**
  * @dev Integer division of two numbers, truncating the quotient.
  */
  function div(uint256 a, uint256 b) internal pure returns (uint256) {
    // assert(b > 0); // Solidity automatically throws 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 Substracts two numbers, throws on overflow (i.e. if subtrahend is greater than minuend).
  */
  function sub(uint256 a, uint256 b) internal pure returns (uint256) {
    assert(b <= a);
    return a - b;
  }

  /**
  * @dev Adds two numbers, throws on overflow.
  */
  function add(uint256 a, uint256 b) internal pure returns (uint256) {
    uint256 c = a + b;
    assert(c >= a);
    return c;
  }
}

/**
 * @title SafeMath32
 * @dev SafeMath library implemented for uint32
 */
library SafeMath32 {

  function mul(uint32 a, uint32 b) internal pure returns (uint32) {
    if (a == 0) {
      return 0;
    }
    uint32 c = a * b;
    assert(c / a == b);
    return c;
  }

  function div(uint32 a, uint32 b) internal pure returns (uint32) {
    // assert(b > 0); // Solidity automatically throws when dividing by 0
    uint32 c = a / b;
    // assert(a == b * c + a % b); // There is no case in which this doesn't hold
    return c;
  }

  function sub(uint32 a, uint32 b) internal pure returns (uint32) {
    assert(b <= a);
    return a - b;
  }

  function add(uint32 a, uint32 b) internal pure returns (uint32) {
    uint32 c = a + b;
    assert(c >= a);
    return c;
  }
}

/**
 * @title SafeMath16
 * @dev SafeMath library implemented for uint16
 */
library SafeMath16 {

  function mul(uint16 a, uint16 b) internal pure returns (uint16) {
    if (a == 0) {
      return 0;
    }
    uint16 c = a * b;
    assert(c / a == b);
    return c;
  }

  function div(uint16 a, uint16 b) internal pure returns (uint16) {
    // assert(b > 0); // Solidity automatically throws when dividing by 0
    uint16 c = a / b;
    // assert(a == b * c + a % b); // There is no case in which this doesn't hold
    return c;
  }

  function sub(uint16 a, uint16 b) internal pure returns (uint16) {
    assert(b <= a);
    return a - b;
  }

  function add(uint16 a, uint16 b) internal pure returns (uint16) {
    uint16 c = a + b;
    assert(c >= a);
    return c;
  }
}

library SafeMath8 {

  function mul(uint8 a, uint8 b) internal pure returns (uint8) {
    if (a == 0) {
      return 0;
    }
    uint8 c = a * b;
    assert(c / a == b);
    return c;
  }

  function div(uint8 a, uint8 b) internal pure returns (uint8) {
    // assert(b > 0); // Solidity automatically throws when dividing by 0
    uint8 c = a / b;
    // assert(a == b * c + a % b); // There is no case in which this doesn't hold
    return c;
  }

  function sub(uint8 a, uint8 b) internal pure returns (uint8) {
    assert(b <= a);
    return a - b;
  }

  function add(uint8 a, uint8 b) internal pure returns (uint8) {
    uint8 c = a + b;
    assert(c >= a);
    return c;
  }
}

2、自增修改

2.1 案例A 簡單變數

//原文1

uint numA;
numA++;

//修改1

import "./safemath.sol";
using SafeMath for uint256;

uint numA;
//numA++;
numA = numA.add(1);

2.2 案例B map變數

//原文2

mapping(address => uint) ownerAppleCount;
ownerAppleCount[msg.sender]++;

//修改2

import "./safemath.sol";
using SafeMath for uint256;

mapping(address => uint) ownerAppleCount;
//ownerAppleCount[msg.sender]++;
ownerAppleCount[msg.sender] = ownerAppleCount[msg.sender].add(1);

2.3 案例C 結構體變數

//原文3

struct Apple {
    uint32 id;	
	uint   weight;
	string color;
}
Apple zhaoApple = Apple(100,150,"red");
zhaoApple.weight++;

//修改3

import "./safemath.sol";
using SafeMath for uint256;
using SafeMath32 for uint32;

struct Apple {
    uint32 id;	
	uint   weight;
	string color;
}
Apple zhaoApple = Apple(100,150,"red");
//zhaoApple.weight++;
zhaoApple.weight = zhaoApple.weight.add(1);

3、自減修改

3.1 案例D

//原文4

uint8 numB;
numB--;

//修改4

import "./safemath.sol";
using SafeMath8 for uint8;

uint8 numB;
numB--;
numB = numB.sub(1);