http://ideone.com/WxuX0r

floor_sqrt.cpp

#include <iostream>
using namespace std;
 
int main() {
  auto sqr=[](int x){return x*x;};
  auto sqrt=[sqr](int x){
    auto center=[](int a,int b){return (a+b)>>1;};
    int low=0<<(sizeof(x)*8/2);
    int top=1<<(sizeof(x)*8/2);
    cout<<"top = "<<top<<endl;
    for(int i=0;i<32;i++){
      cout<<"low = "<<low<<"     top = "<<top<<endl;
      int c=center(low,top);cout<<c<<endl;
      (c*c<=x?low:top)=c;
      if(sqr(c+0)<=x)if(sqr(c+1)>x)return c;
    }
    return -1;
  };
  cout<<"result = "<<sqrt(sqr(31000))<<endl;;
  return 0;
}