C++ BigInteger Library

// header files
#include <cstdio>
#include <string>
#include <algorithm>
#include <iostream>
using namespace std;
struct Bigint
{
    // representations and structures
    string a; // to store the digits
    int sign; // sign = -1 for negative numbers, sign = 1 otherwise
    // constructors
    Bigint() {} // default constructor
    Bigint( string b )
    {
        (*this) = b;    // constructor for string
    }
    // some helpful methods
    int size()   // returns number of digits
    {
        return a.size();
    }
    Bigint inverseSign()   // changes the sign
    {
        sign *= -1;
        return (*this);
    }
    Bigint normalize( int newSign )   // removes leading 0, fixes sign
    {
        for( int i = a.size() - 1; i > 0 && a[i] == '0'; i-- )
            a.erase(a.begin() + i);
        sign = ( a.size() == 1 && a[0] == '0' ) ? 1 : newSign;
        return (*this);
    }
    // assignment operator
    void operator = ( string b )   // assigns a string to Bigint
    {
        a = b[0] == '-' ? b.substr(1) : b;
        reverse( a.begin(), a.end() );
        this->normalize( b[0] == '-' ? -1 : 1 );
    }
    // conditional operators
    bool operator < ( const Bigint &b ) const   // less than operator
    {
        if( sign != b.sign )
            return sign < b.sign;
        if( a.size() != b.a.size() )
            return sign == 1 ? a.size() < b.a.size() : a.size() > b.a.size();
        for( int i = a.size() - 1; i >= 0; i-- )
            if( a[i] != b.a[i] )
                return sign == 1 ? a[i] < b.a[i] : a[i] > b.a[i];
        return false;
    }
    bool operator == ( const Bigint &b ) const   // operator for equality
    {
        return a == b.a && sign == b.sign;
    }

    // mathematical operators
    Bigint operator + ( Bigint b )   // addition operator overloading
    {
        if( sign != b.sign )
            return (*this) - b.inverseSign();
        Bigint c;
        for(int i = 0, carry = 0; i<a.size() || i<b.size() || carry; i++ )
        {
            carry+=(i<a.size() ? a[i]-48 : 0)+(i<b.a.size() ? b.a[i]-48 : 0);
            c.a += (carry % 10 + 48);
            carry /= 10;
        }
        return c.normalize(sign);
    }
    Bigint operator - ( Bigint b )   // subtraction operator overloading
    {
        if( sign != b.sign )
            return (*this) + b.inverseSign();
        int s = sign;
        sign = b.sign = 1;
        if( (*this) < b )
            return ((b - (*this)).inverseSign()).normalize(-s);
        Bigint c;
        for( int i = 0, borrow = 0; i < a.size(); i++ )
        {
            borrow = a[i] - borrow - (i < b.size() ? b.a[i] : 48);
            c.a += borrow >= 0 ? borrow + 48 : borrow + 58;
            borrow = borrow >= 0 ? 0 : 1;
        }
        return c.normalize(s);
    }
    Bigint operator * ( Bigint b )   // multiplication operator overloading
    {
        Bigint c("0");
        for( int i = 0, k = a[i] - 48; i < a.size(); i++, k = a[i] - 48 )
        {
            while(k--)
                c = c + b; // ith digit is k, so, we add k times
            b.a.insert(b.a.begin(), '0'); // multiplied by 10
        }
        return c.normalize(sign * b.sign);
    }
    Bigint operator / ( Bigint b )   // division operator overloading
    {
        if( b.size() == 1 && b.a[0] == '0' )
            b.a[0] /= ( b.a[0] - 48 );
        Bigint c("0"), d;
        for( int j = 0; j < a.size(); j++ )
            d.a += "0";
        int dSign = sign * b.sign;
        b.sign = 1;
        for( int i = a.size() - 1; i >= 0; i-- )
        {
            c.a.insert( c.a.begin(), '0');
            c = c + a.substr( i, 1 );
            while( !( c < b ) )
                c = c - b, d.a[i]++;
        }
        return d.normalize(dSign);
    }
    Bigint operator % ( Bigint b )   // modulo operator overloading
    {
        if( b.size() == 1 && b.a[0] == '0' )
            b.a[0] /= ( b.a[0] - 48 );
        Bigint c("0");
        b.sign = 1;
        for( int i = a.size() - 1; i >= 0; i-- )
        {
            c.a.insert( c.a.begin(), '0');
            c = c + a.substr( i, 1 );
            while( !( c < b ) )
                c = c - b;
        }
        return c.normalize(sign);
    }

    // output method
    void print()
    {
        if( sign == -1 )
            putchar('-');
        for( int i = a.size() - 1; i >= 0; i-- )
            putchar(a[i]);
    }
};
int main()
{
    Bigint a, b, c; // declared some Bigint variables
    /////////////////////////
    // taking Bigint input //
    /////////////////////////
    string input; // string to take input
    cin >> input; // take the Big integer as string
    a = input; // assign the string to Bigint a
    cin >> input; // take the Big integer as string
    b = input; // assign the string to Bigint b

    //////////////////////////////////
    // Using mathematical operators //
    //////////////////////////////////
    c = a + b; // adding a and b
    c.print(); // printing the Bigint
    puts(""); // newline
    c = a - b; // subtracting b from a
    c.print(); // printing the Bigint
    puts(""); // newline
    c = a * b; // multiplying a and b
    c.print(); // printing the Bigint
    puts(""); // newline
    c = a / b; // dividing a by b
    c.print(); // printing the Bigint
    puts(""); // newline
    c = a % b; // a modulo b
    c.print(); // printing the Bigint
    puts(""); // newline
    /////////////////////////////////
    // Using conditional operators //
    /////////////////////////////////
    if( a == b )
        puts("equal"); // checking equality
    else
        puts("not equal");
    if( a < b )
        puts("a is smaller than b"); // checking less than operator
    return 0;
}