Calculate 2^x

#include<iostream>
#include <vector>


void TwoPowerNoJutsu(std::vector<short> &source, short expo) {
    if (expo <= 3) {
        switch (expo) {
        case 0:
            source.emplace_back(1);
            return;
        case 1:
            source.emplace_back(2);
            return;
        case 2:
            source.emplace_back(4);
            return;
        case 3:
            source.emplace_back(8);
            return;
        }
    }
    short index = 0, remainder = 0, temp=0;
    source.emplace_back(6);
    source.emplace_back(1);
    while (expo > 4) {
        source[index] = source[index] * 2 + temp;
        temp = 0;
        if (source[index] >= 10) {
            remainder = source[index] / 10;
            if (index +1== source.size()) {
                source.emplace_back(remainder);
                source[index] = source[index] % 10;
                index=0;
                expo--;
            }
            else{
                source[index + 1] = source[index + 1] * 2 + remainder;
                if (source[index + 1] >= 10) {
                    temp = source[index + 1] / 10;
                    source[index + 1] = source[index + 1] % 10;
                }
                source[index] = source[index] % 10;
                index = index + 2;
                if (index >= source.size()) {
                    source.emplace_back(temp);
                    temp = 0;
                }
            }
        }
        else {
            index++;
        }
        if (index >= source.size()) {
            index = 0;
            expo--;
        }
    }
    if (source[source.size() - 1] == 0) {
        source.pop_back();
    }

}
void LogNoJutsu(std::vector<short> source, short expo) {
    std::cout << "2^" << expo << " = ";
    for (int i = source.size()-1; i >=0 ; i--) {
        std::cout << source[i];
    }
    std::cout<<"\n";
}

short main() {
    std::vector<short> a;
    short expo = 128;
    for (int i = 0; i <= expo; i++) {
        TwoPowerNoJutsu(a, i);
        LogNoJutsu(a, i);
        a.clear();
        a.empty();
    }
    std::cin.get();
    return 0;
}