大整数类BIGN的设计与实现 C++高精度模板

众所周知，C++中储存能力最大的unsigned long long 也是有着一个上限，如果我们想计算非常大的整数时，就不知所措了，所以，我写了一个高精度类，允许大整数的四则运算

这个类利用字符串进行输入输出，并利用数组进行储存与处理，通过模拟四则运算，可以计算很大的整数的加减乘除比大小。

贴上我的代码：

#include<string> #include<iostream> #include<iosfwd> #include<cmath> #include<cstring> #include<stdlib.h> #include<stdio.h> #include<cstring> #define MAX_L 2005 //最大长度，可以修改 using namespace std;  class bign { public:     int len, s[MAX_L];//数的长度，记录数组 //构造函数     bign();     bign(const char*);     bign(int);     bool sign;//符号 1正数 0负数     string toStr() const;//转化为字符串，主要是便于输出     friend istream& operator>>(istream &,bign &);//重载输入流     friend ostream& operator<<(ostream &,bign &);//重载输出流 //重载复制     bign operator=(const char*);     bign operator=(int);     bign operator=(const string); //重载各种比较     bool operator>(const bign &) const;     bool operator>=(const bign &) const;     bool operator<(const bign &) const;     bool operator<=(const bign &) const;     bool operator==(const bign &) const;     bool operator!=(const bign &) const; //重载四则运算     bign operator+(const bign &) const;     bign operator++();     bign operator++(int);     bign operator+=(const bign&);     bign operator-(const bign &) const;     bign operator--();     bign operator--(int);     bign operator-=(const bign&);     bign operator*(const bign &)const;     bign operator*(const int num)const;     bign operator*=(const bign&);     bign operator/(const bign&)const;     bign operator/=(const bign&); //四则运算的衍生运算     bign operator%(const bign&)const;//取模（余数）     bign factorial()const;//阶乘     bign Sqrt()const;//整数开根（向下取整）     bign pow(const bign&)const;//次方 //一些乱乱的函数     void clean();     ~bign(); }; #define max(a,b) a>b ? a : b #define min(a,b) a<b ? a : b  bign::bign() {     memset(s, 0, sizeof(s));     len = 1;     sign = 1; }  bign::bign(const char *num) {     *this = num; }  bign::bign(int num) {     *this = num; }  string bign::toStr() const {     string res;     res = "";     for (int i = 0; i < len; i++)         res = (char)(s[i] + '0') + res;     if (res == "")         res = "0";     if (!sign&&res != "0")         res = "-" + res;     return res; }  istream &operator>>(istream &in, bign &num) {     string str;     in>>str;     num=str;     return in; }  ostream &operator<<(ostream &out, bign &num) {     out<<num.toStr();     return out; }  bign bign::operator=(const char *num) {     memset(s, 0, sizeof(s));     char a[MAX_L] = "";     if (num[0] != '-')         strcpy(a, num);     else         for (int i = 1; i < strlen(num); i++)             a[i - 1] = num[i];     sign = !(num[0] == '-');     len = strlen(a);     for (int i = 0; i < strlen(a); i++)         s[i] = a[len - i - 1] - 48;     return *this; }  bign bign::operator=(int num) {     if (num < 0)         sign = 0, num = -num;     else         sign = 1;     char temp[MAX_L];     sprintf(temp, "%d", num);     *this = temp;     return *this; }  bign bign::operator=(const string num) {     const char *tmp;     tmp = num.c_str();     *this = tmp;     return *this; }  bool bign::operator<(const bign &num) const {     if (sign^num.sign)         return num.sign;     if (len != num.len)         return len < num.len;     for (int i = len - 1; i >= 0; i--)         if (s[i] != num.s[i])             return sign ? (s[i] < num.s[i]) : (!(s[i] < num.s[i]));     return !sign; }  bool bign::operator>(const bign&num)const {     return num < *this; }  bool bign::operator<=(const bign&num)const {     return !(*this>num); }  bool bign::operator>=(const bign&num)const {     return !(*this<num); }  bool bign::operator!=(const bign&num)const {     return *this > num || *this < num; }  bool bign::operator==(const bign&num)const {     return !(num != *this); }  bign bign::operator+(const bign &num) const {     if (sign^num.sign)     {         bign tmp = sign ? num : *this;         tmp.sign = 1;         return sign ? *this - tmp : num - tmp;     }     bign result;     result.len = 0;     int temp = 0;     for (int i = 0; temp || i < (max(len, num.len)); i++)     {         int t = s[i] + num.s[i] + temp;         result.s[result.len++] = t % 10;         temp = t / 10;     }     result.sign = sign;     return result; }  bign bign::operator++() {     *this = *this + 1;     return *this; }  bign bign::operator++(int) {     bign old = *this;     ++(*this);     return old; }  bign bign::operator+=(const bign &num) {     *this = *this + num;     return *this; }  bign bign::operator-(const bign &num) const {     bign b=num,a=*this;     if (!num.sign && !sign)     {         b.sign=1;         a.sign=1;         return b-a;     }     if (!b.sign)     {         b.sign=1;         return a+b;     }     if (!a.sign)     {         a.sign=1;         b=bign(0)-(a+b);         return b;     }     if (a<b)     {         bign c=(b-a);         c.sign=false;         return c;     }     bign result;     result.len = 0;     for (int i = 0, g = 0; i < a.len; i++)     {         int x = a.s[i] - g;         if (i < b.len) x -= b.s[i];         if (x >= 0) g = 0;         else         {             g = 1;             x += 10;         }         result.s[result.len++] = x;     }     result.clean();     return result; }  bign bign::operator * (const bign &num)const {     bign result;     result.len = len + num.len;      for (int i = 0; i < len; i++)         for (int j = 0; j < num.len; j++)             result.s[i + j] += s[i] * num.s[j];      for (int i = 0; i < result.len; i++)     {         result.s[i + 1] += result.s[i] / 10;         result.s[i] %= 10;     }     result.clean();     result.sign = !(sign^num.sign);     return result; }  bign bign::operator*(const int num)const {     bign x = num;     bign z = *this;     return x*z; } bign bign::operator*=(const bign&num) {     *this = *this * num;     return *this; }  bign bign::operator /(const bign&num)const {     bign ans;     ans.len = len - num.len + 1;     if (ans.len < 0)     {         ans.len = 1;         return ans;     }      bign divisor = *this, divid = num;     divisor.sign = divid.sign = 1;     int k = ans.len - 1;     int j = len - 1;     while (k >= 0)     {         while (divisor.s[j] == 0) j--;         if (k > j) k = j;         char z[MAX_L];         memset(z, 0, sizeof(z));         for (int i = j; i >= k; i--)             z[j - i] = divisor.s[i] + '0';         bign dividend = z;         if (dividend < divid) { k--; continue; }         int key = 0;         while (divid*key <= dividend) key++;         key--;         ans.s[k] = key;         bign temp = divid*key;         for (int i = 0; i < k; i++)             temp = temp * 10;         divisor = divisor - temp;         k--;     }     ans.clean();     ans.sign = !(sign^num.sign);     return ans; }  bign bign::operator/=(const bign&num) {     *this = *this / num;     return *this; }  bign bign::operator%(const bign& num)const {     bign a = *this, b = num;     a.sign = b.sign = 1;     bign result, temp = a / b*b;     result = a - temp;     result.sign = sign;     return result; }  bign bign::pow(const bign& num)const {     bign result = 1;     for (bign i = 0; i < num; i++)         result = result*(*this);     return result; }  bign bign::factorial()const {     bign result = 1;     for (bign i = 1; i <= *this; i++)         result *= i;     return result; }  void bign::clean() {     if (len == 0) len++;     while (len > 1 && s[len - 1] == '/0')         len--; }  bign bign::Sqrt()const {     if(*this<0)return -1;     if(*this<=1)return *this;     bign l=0,r=*this,mid;     while(r-l>1)     {         mid=(l+r)/2;         if(mid*mid>*this)             r=mid;         else              l=mid;     }     return l; }  bign::~bign() { }  bign num0,num1,res;  int main() {     cin>>num0>>num1;     res=num0+num1;     cout<<res<<endl;      num0=5;     num1="71";     res=num0-num1;     cout<<res<<endl;      res=num0.Sqrt();     cout<<res<<endl;      res=num0.pow(5);     cout<<res<<endl;     return 0; }