C++实现大数运算（加减乘除求余）
前言：
只有部分GCC编译器支持int128，而我们平常使用的软件，最大只有_int64.当这些不够用时，我们该怎么办？
我本身想写代码实现整数型大数据的加减乘除和求余，结果写着写着想着连小数运算的也一起写上（反正加的代码不多）
电脑是死的，人是活的，当数据超出范围时，我们可以想其他方法去算，在这里，我使用string类来存数据，string类的容量足够大，相信够一般大数据使用了吧。
编译软件：vs2013
程序功能： 大型整数、小数的加、减、乘、除、求余
代码：
main.cpp
#include
#include
#include
#include "large.h"
using namespace std;
int main()
{
char ch;
string m_snum1, m_snum2;
while (cin>>m_snum1>>ch>>m_snum2)
{
large _large(m_snum1, ch, m_snum2);
}
return 0;
} large.h
#include
#include
using namespace std;
class large
{
public:
large(){}
large(string m_str1, char m_ch, string m_str2); //两数的运算
inline int compare(string str1, string str2); //相等返回0，大于返回1，小于返回-1
string SUB_INT(string str1, string str2); //高精度减法
string ADD_INT(string str1, string str2); //高精度加法
string MUL_INT(string str1, string str2); //高精度乘法
string DIVIDE_INT(string str1, string str2, int flag); //高精度除法，flag==1,返回商;flag==0时，返回余数
string DIV_INT(string str1, string str2); //高精度除法，返回商
string MOD_INT(string str1, string str2); //高精度除法，返回余数
large(large &e); //拷贝构造
~large(){}; //析构函数
}; large.cpp
#include
#include
#include
#include "large.h"
using namespace std;
large::large(string m_str1, char m_ch, string m_str2)//两数的运算
{
int m_ilocation1 ;
int m_ilocation2 ;
string m_res;
int m_istr;
if (m_str1.find_first_of(".") == -1)
m_ilocation1 = 0;
else
m_ilocation1 = m_str1.length() - m_str1.find_first_of(".") - 1;
if (m_str2.find_first_of(".") == -1)
m_ilocation2 = 0;
else
m_ilocation2 = m_str2.length() - m_str2.find_first_of(".") - 1;
if (m_ilocation1 == 0 && m_ilocation2 == 0)
{
switch (m_ch)
{
case'+':
m_res = ADD_INT(m_str1, m_str2); break;
case'-':
m_res = SUB_INT(m_str1, m_str2); break;
case'*':
m_res = MUL_INT(m_str1, m_str2); break;
case'/':
m_res = DIV_INT(m_str1, m_str2); break;
case'%':
m_res = MOD_INT(m_str1, m_str2); break;
default:
break;
}
}
else
{
int m_ilocat = m_ilocation1 - m_ilocation2;
int m_ilocation3;
if (m_ilocation1!=0)
m_str1.erase(m_str1.find_first_of("."), m_str1.find_first_not_of(".") + 1);
if (m_ilocation2!=0)
m_str2.erase(m_str2.find_first_of("."), m_str2.find_first_not_of(".") + 1);
switch (m_ch)
{
case'+':
if (m_ilocat >= 0)
{
for (int i = 0; i < m_ilocat; i++)
m_str2 = m_str2 + '0';
m_ilocation3 = m_ilocation1;
}
else
{
for (int i = 0; i < -m_ilocat; i++)
m_str1 = m_str1 + '0';
m_ilocation3 = m_ilocation2;
}
m_res = ADD_INT(m_str1, m_str2);
m_istr = m_res.length();
for (int i = 0; i < m_ilocation3; i++)
m_istr = m_istr - 1;
m_res.insert(m_istr, ".");
break;
case'-':
if (m_ilocat >= 0)
{
for (int i = 0; i < m_ilocat; i++)
m_str2 = m_str2 + '0';
m_ilocation3 = m_ilocation1;
}
else
{
for (int i = 0; i < -m_ilocat; i++)
m_str1 = m_str1 + '0';
m_ilocation3 = m_ilocation2;
}
m_res = SUB_INT(m_str1, m_str2);
m_istr = m_res.length();
for (int i = 0; i < m_ilocation3; i++)
m_istr = m_istr - 1;
m_res.insert(m_istr, ".");
break;
case'*':
m_ilocation3=m_ilocation1+m_ilocation2;
m_res = MUL_INT(m_str1, m_str2);
m_istr = m_res.length();
for (int i = 0; i < m_ilocation3; i++)
m_istr = m_istr - 1;
m_res.insert(m_istr, "."); break;
case'/':
if (m_ilocat >= 0)
{
for (int i = 0; i < m_ilocat; i++)
m_str2 = m_str2 + '0';
}
else
{
for (int i = 0; i < -m_ilocat; i++)
m_str1 = m_str1 + '0';
}
m_res = DIV_INT(m_str1, m_str2); break;
case'%':
m_res = MOD_INT(m_str1, m_str2); break;
default:
break;
}
}
cout << endl;
cout << m_res << endl;
}
inline int large::compare(string str1, string str2) //相等返回0，大于返回1，小于返回-1
{
if (str1.size() > str2.size())
return 1;
else if (str1.size() < str2.size())
return -1;
else return str1.compare(str2); //若长度相等，则从头到尾按位比较
}
string large::ADD_INT(string str1, string str2) //高精度加法
{
int sign = 1;//sign为符号为
string str;
if (str1[0] == '-')
{
if (str2[0] == '-') //负负
{
sign = -1;
str = ADD_INT(str1.erase(0, 1), str2.erase(0, 1));//erase(first,last);删除从first到last之间的字符
}
else //负正
{
str = SUB_INT(str2, str1.erase(0, 1));
}
}
else
{
if (str2[0] == '-') //正负
{
str = SUB_INT(str1, str2.erase(0, 1));
}
else //正正，把两个整数对齐，短整数前面加0补齐
{
string::size_type L1, L2; //string::size_type抽象意义是尺寸单位类型
int i;
L1 = str1.size();
L2 = str2.size();
if (L1 < L2)
{
for (i = 0; i < L2 - L1; i++)
str1 = "0" + str1;
}
else
{
for (i = 0; i < L1 - L2; i++)
str2 = "0" + str2;
}
int int1 = 0, int2 = 0; //int2记录进位
for (i = str1.size() - 1; i >= 0; i--)
{
int1 = (int(str1[i]) - '0' + int(str2[i]) - '0' + int2) % 10;
int2 = (int(str1[i]) - '0' + int(str2[i]) - '0' + int2) / 10;
str = char(int1 + '0') + str;
}
if (int2 != 0)str = char(int2 + '0') + str;
}
}
//运算符处理符号
if ((sign == -1) && (str[0] != '0'))str = "-" + str;
return str;
}
string large::SUB_INT(string str1, string str2) //高精度减法
{
int sign = 1; //sign为符号位
string str;
int i, j;
if (str2[0] == '-')
{
str = ADD_INT(str1, str2.erase(0, 1));
}
else
{
int res = compare(str1, str2);
if (res == 0)return "0";
if (res < 0)
{
sign = -1;
string temp = str1;
str1 = str2;
str2 = temp;
}
string::size_type tempint;
tempint = str1.size() - str2.size();
for (i = str2.size() - 1; i >= 0; i--)
{
if (str1[i + tempint] < str2[i]) //借位
{
j = 1;
while (1)
{
if (str1[tempint - j + i] == '0')
{
str1[i + tempint - j] = '9';
j++;
}
else
{
str1[i + tempint - j] = char(int(str1[i + tempint - j]) - 1);
break;
}
}
str = char(str1[i + tempint] - str2[i] + ':') + str;
}
else
{
str = char(str1[i + tempint] - str2[i] + '0') + str;
}
}
for (i = tempint - 1; i >= 0; i--)
str = str1[i] + str;
}
//去出结果中多余的前导0
str.erase(0, str.find_first_not_of('0'));
if (str.empty())str = "0";
if ((sign == -1) && (str[0] != '0'))str = "-" + str;
return str;
}
string large::MUL_INT(string str1, string str2) //高精度乘法
{
int sign = 1;
string str = "0"; //记录当前值
if (str1[0] == '-')
{
sign *= -1;
str1 = str1.erase(0, 1);
}
if (str2[0] == '-')
{
sign *= -1;
str2 = str2.erase(0, 1);
}
int i, j;
string::size_type L1, L2;
L1 = str1.size();
L2 = str2.size();
for (i = L2 - 1; i >= 0; i--) //模拟手工乘法竖式
{
string tempstr;
int int1 = 0, int2 = 0, int3 = int(str2[i]) - '0';
if (int3 != 0)
{
for (j = 1; j <= (int)(L2 - 1 - i); j++)
tempstr = "0" + tempstr;
for (j = L1 - 1; j >= 0; j--)
{
int1 = (int3*(int(str1[j]) - '0') + int2) % 10;
int2 = (int3*(int(str1[j]) - '0') + int2) / 10;
tempstr = char(int1 + '0') + tempstr;
}
if (int2 != 0)tempstr = char(int2 + '0') + tempstr;
}
str = ADD_INT(str, tempstr);
}
//去除结果中的前导0
str.erase(0, str.find_first_not_of("0"));
if (str.empty())str = "0";
if ((sign == -1) && (str[0] != '0'))str = "-" + str;
return str;
}
string large::DIVIDE_INT(string str1, string str2, int flag) //高精度除法，flag==1,返回商;flag==0时，返回余数
{
string quotient, residue; //定义商和余数
int sign1 = 1, sign2 = 1;
if (str2 == "0") //判断除数是否为0
{
quotient = "ERROR!";
residue = "ERROR!";
if (flag == 1)return quotient;
else return residue;
}
if (str1 == "0") //判断被除数是否为0
{
quotient = "0";
residue = "0";
}
if (str1[0] == '-')
{
str1 = str1.erase(0, 1);
sign1 *= -1;
sign2 = -1;
}
if (str2[0] == '-')
{
str2 = str2.erase(0, 1);
sign1 *= -1;
}
int res = compare(str1, str2);
if (res < 0)
{
quotient = "0";
residue = str1;
}
else if (res == 0)
{
quotient = "1";
residue = "0";
}
else
{
string::size_type L1, L2;
L1 = str1.size();
L2 = str2.size();
string tempstr;
tempstr.append(str1, 0, L2 - 1); //将str1中为值0到L2-1的字符串追加到tempstr
for (int i = L2 - 1; i < L1; i++) //模拟手工除法竖式
{
tempstr = tempstr + str1[i];
tempstr.erase(0, tempstr.find_first_not_of('0')); //在字符串中查找第一个与'0'不匹配的字符，返回它的位置
if (tempstr.empty())tempstr = "0"; //q.empty()，当队列空时，返回true
for (char ch = '9'; ch >= '0'; ch--) //试商
{
string str;
str = str + ch;
if (compare(MUL_INT(str2, str), tempstr) <= 0)
{
quotient = quotient + ch;
tempstr = SUB_INT(tempstr, MUL_INT(str2, str));
break;
}
}
}
residue = tempstr;
}
//去除结果中的前导0
quotient.erase(0, quotient.find_first_not_of("0"));
if (quotient.empty())quotient = "0";
if ((sign1 == -1) && (quotient[0] != '0'))quotient = "-" + quotient;
if ((sign2 == -1) && (residue[0] != '0'))residue = "-" + residue;
if (flag == 1)return quotient;
else
return residue;
}
string large::DIV_INT(string str1, string str2) //高精度除法，返回商
{
return DIVIDE_INT(str1, str2, 1);
}
string large::MOD_INT(string str1, string str2) //高精度除法，返回余数
{
return DIVIDE_INT(str1, str2, 0);
} 运行结果展示：
例子：多位数的小数相加：
这下子就不怕数据超出范围了，欢迎一起探讨，一起交流。