Long integers handled with strings

t11e26.longNatural.cpp

// t11e26.longNatural.cpp
// juanfc 2023-11-22
// Juan Falgueras, 1997-11-25 al 2003-12-05
// 

#include <iostream>
#include <iomanip>
using namespace std;

void test(string s1, string s2);

int main() {
    test("1", "1");
    test("2", "10");
    test("122345", "90");
    return 0;
}

// PROTOTYPES
string longAdding(string a, string b, int BASE=10);
string longMult(string a, string b, int BASE=10);
string longPow(string a, string b, int BASE = 10);

void test(string s1, string s2)
{
    int w = s1.length()+s2.length()+1;

    cout << "    " << setw(w) << s1 << endl;
    cout << "    " << setw(w) << s2 << " = "<< endl;
    cout << "+ : " << setw(w) << longAdding(s1,s2) << endl;
    cout << "* : " << setw(w) << longMult(s1,s2) <<   endl;
    cout << "^ : " << setw(w) << longPow(s1,s2) << endl << endl;
}


// BODYS
void stringRev(string& s);

string longAdding(string a, string b, int BASE)
{
    string dest;
    const int OO = ((int)'0');
    stringRev(a);
    stringRev(b);
    int la = a.length();
    int lb = b.length();
    if (la < lb)
        for (int i = la; i < lb; ++i)
            a += '0';
    else
        for (int i = lb; i < la; ++i)
            b += '0';
    int carry = 0;
    la = a.length();
    for (int i=0;  i < la ; i++) {
        int t = carry;
        t += a[i] - OO;
        t += b[i] - OO;
        dest += (t % BASE) + OO;
        carry = t / BASE;
    }
    if (carry > 0)
        dest += '1';
    stringRev(dest);
    return dest;
} // LongAdding


string longMult(string a, string b, int BASE)
{
    string dest;
    const int O = ((int)'0');
    int lena, lenb, lend;

    lena= a.length();
    lenb= b.length();
    stringRev(a);
    stringRev(b);

    lend= lena+lenb+1;
    for (int i=0; i < lend; i++)
        dest += '0';

    for (int i= 0; i < lena; i++) {
        for (int j= 0; j < lenb; j++) {
            int carry;
            int t= ((int)dest[i+j]-O) + ((int)a[i]-O) * ((int)b[j]-O);
            dest[i+j]= (char)(t % BASE + O);
            carry= t / BASE;

            int k= 1;
            do {
                t= ((int)dest[i+j+k]-O) + carry;
                dest[i+j+k]= (char)(t % BASE + O);
                carry= t / BASE;
                ++k;
            } while (carry > 0);
        } // for
    } // for
    int j= dest.length() - 1;
    while (j > 0 and dest[j] == '0')
        --j;
    dest = dest.substr(0, j+1);
    stringRev(dest);
    return dest;
} // longMult

string longPow(string a, string b, int BASE)
{
    string cnt = "0";
    string r = "1";
    while (cnt != b) {
        r = longMult(a, r, BASE);
        cnt = longAdding(cnt, "1");
    }
    return r;
} // longPow

void stringRev(string& s)
{
    int i = 0;
    int j = s.length()-1;
    while (i<j) {
        char t = s[i];
        s[i] = s[j];
        s[j] = t;
        ++i; --j;
    }
}