// \begin{verbatim}
    #include<cstdio>
    #include<iomanip>
    #include<cassert>
    #include<string>
    #include<cmath>
    #include<iostream>
    #include<sstream>
    #include<stdio.h>
    #include<stdlib.h>
     using namespace std;

  const int N = 30; // limits the depth of the recursion

  float guess(float x, float b, int M)
   {
    assert(x > 0.0 and b > 1.0);
    if(x == 1) return 0;
    else if(M <= 0) return 0; // Really?  Shouldn't it be 1?  Does it matter?
    else if(x < 1) return -guess(1/x,b,M);
    else if(x > b) return 1 + guess(x/b,b,M); 
    else if(x < b) return guess(x*x,b,M-1)/2;
    else return 1.0;
   }

  float guess(float x, float b)
   {
    cout << "Computing guess(" << x << "," << b << ")" << endl;
    return guess(x,b,N);
   }

  int main()
   {
    float x;
    cout << "Enter a positive number x:  ";
    cin >> x;
    cout << endl;
    float b;
    cout << "Enter a number larger than 1:  ";
    cin >> b;
    cout << endl;
    cout << guess(x,b) << endl;
    return 1;
   }
// \end{verbatim}