first draft of a simple roman calculator

roman.cpp

#include <iostream>
#include <vector>
#include <map>
#include <string>
#include <cmath>
#include <regex>
#include <sstream>

using namespace std;

string toString(const int& i) {
    stringstream s;
    s << i;
    return s.str();
}

string roman_from_value(const int& inum) {
    int temp {inum};
    string result;

    int m = inum / 1000;
    for(int i=0; i<m; ++i) result += "M";
    temp = temp - m*1000;

    if(temp >= 900) {
        result += "CM";
        temp -= 900;
    }
    else if(temp >= 500) {
        result += "D";
        temp -= 500;
    }
    else if(temp >=400) {
        result += "CD";
        temp -= 400;
    }
    if(temp >= 100) {
        int c = temp/100;
        for(int i=0; i<c; ++i) result += "C";
        temp = temp - c*100;
    }

    if(temp >= 90) {
        result += "XC";
        temp -= 90;
    }
    else if(temp >= 50) {
        result += "L";
        temp -= 50;
    }
    else if(temp >= 40) {
        result += "XL";
        temp -= 40;
    }
    if(temp >= 10) {
        int x = temp/10;
        for(int i=0; i<x; ++i) result += "X";
        temp = temp - x*10;
    }

    if(temp == 9) {
        result += "IX";
        temp -= 9;
    }
    else if(temp >= 5) {
        result += "V";
        temp -= 5;
    }
    else if(temp == 4) {
        result += "IV";
        temp -= 4;
    }
    if(temp >= 1) {
        int i = temp/1;
        for(int j=0; j<i; ++j) result += "I";
    }

    return result;
}

int value_from_roman(const string& rval) {
    map<char,int> roman;
    roman['I'] = 1;
    roman['V'] = 5;
    roman['X'] = 10;
    roman['L'] = 50;
    roman['C'] = 100;
    roman['D'] = 500;
    roman['M'] = 1000;
    int temp {0};
    char previous_char {' '};
    for(int i=rval.size()-1; i>=0; --i) {
        if((rval[i] != previous_char) && (roman[rval[i]] < temp)) {
            temp -= roman[rval[i]];
        } else {
            temp += roman[rval[i]];
        }
        previous_char = rval[i];
    }
    return temp;
}

class Roman_invalid {};

class Roman_int {
    public:
        Roman_int() {};
        Roman_int(const string& rnum);
        Roman_int(const int& inum);
        int as_int() const { return ival; };
        string as_roman() const { return rval; };
    private:
        string rval;
        int ival;
};

Roman_int::Roman_int(const string& rnum) {
    rval = rnum;
    ival = value_from_roman(rval);
}

Roman_int::Roman_int(const int& inum) {
    rval = roman_from_value(inum);
    ival = inum;
}

ostream& operator<<(ostream& os, const Roman_int& r) {
    return os << r.as_roman();
}

istream& operator>>(istream& is, Roman_int& r) {
    string rval;
    is >> rval;
    if(!is) return is;
    regex re("^[MDCLXVI]+");
    if(regex_match(rval, re) != 1) throw Roman_invalid {};
    r = Roman_int(rval);
    return is;
}

int operator+(const Roman_int& r1, const Roman_int& r2) {
    return r1.as_int() + r2.as_int();
}

int operator-(const Roman_int& r1, const Roman_int& r2) {
    return r1.as_int() - r2.as_int();
}

int operator*(const Roman_int& r1, const Roman_int& r2) {
    return r1.as_int() * r2.as_int();
}

int main() {
    cout << "Roman Calculator" << endl;
    try {
        Roman_int r1, r2, result;
        char op;
        while(cin >> r1 >> op >> r2) {
            if(op == '+') result = Roman_int(r1+r2);
            else if(op == '-') result = Roman_int(r1-r2);
            else if(op == '*') result = Roman_int(r1*r2);
            else {
                cerr << "Error detected. Exiting..." << endl;
            }
            cout << r1 << op << r2 << "=" << result << endl
                 << r1.as_int() << op << r2.as_int() << '=' << result.as_int() << endl;
        }
        cout << "Exiting..." << endl;
    } catch (Roman_invalid) {
        cerr << "Invalid Roman detected. Exiting." << endl;
        return 1;
    }
    return 0;
}