Sacar la raiz digital de un numero en c++

#include < iostream >
#include < string >
#include < sstream >
#include < fstream >
using namespace std;
main()
{
fstream io("roots.in",ios::in | ios::out);
string a_x1;
while(cin>>a_x1)
{if(a_x1=="0"){break;break;}
a:
if(a_x1.size()>1)
{ int a_x2=0;

for(int i=0;i
a_x2+=(int)a_x1[i] - 48;

}
a_x1.clear();
if(a_x2<10 )
{
cout< }

else {
stringstream out;
out << a_x2;
a_x1 = out.str();
goto a;}
}
}
getchar();
}