Question

Question: I am getting a few errors but I'm not quite sure what I messed up on, if you could take a look and what I should change I would appreciate it. I have included the context of my objective.

Write your own square root function named double my_sqrt_1(double n) using the following pseudocode:

if n < 1 then lower_bound is n, otherwise lower_bound is

      1 + (n – 1) / 2 – (n – 1)² / 8

upper_bound is (n + 1) / 2

repeat 10 times:

      midpoint = average of upper_bound and lower_bound

      if midpoint² > n then upper_bound = midpoint

      if midpoint² < n then lower_bound = midpoint

return midpoint

and then write a main which prints n, sqrt(n), and my_sqrt_1(n) for n =

π times 10 to the k^th power for k = -100, -10, -1, 0, 1, 10, and 100. Use this C++11 code (which may not work on Visual Studio):

      for(auto k : {-100, -10, -1, 0, 1, 10, 100}){

                  n = M_PI * pow(10.0, k);

                  //cout goes here

      }

My code:

#include "std_lib_facilities_4.h"

  

double my_sqrt_1(double n)

{

  

double lower_bound;

double upper_bound;

double midpoint;

for (int iterations=0; iterations<=10;)

{

if (n<1)

{

lower_bound = n;

upper_bound= (n+1)/2;

midpoint = (lower_bound+upper_bound)/2;

if (midpoint*midpoint>n)

{

upper_bound= midpoint;

}

if (midpoint*midpoint<n)

{

lower_bound=midpoint;

}

return midpoint;

}

  

if (n>1)

lower_bound = 1+(n-1)/2-(n-1)*(n-1)/8;

upper_bound = (n+1)/2;

midpoint = (lower_bound+upper_bound)/2;

if (midpoint*midpoint>n)

{

upper_bound= midpoint;

}

if (midpoint*midpoint<n)

{

lower_bound=midpoint;

}

return midpoint;

  

iterations= iterations += 1;

  

}

int main();

{

for(auto k: {-100,-10,-1,0,1,10,100})

{

n= M_PI*pow(10.0,k);

  

cout << n <<"\n";

cout << sqrt(n) <<"\n";

cout << my_sqrt_1(n)<< "\n";

}

}

}

Answer 1

Modified Code

#include<iostream>

#include <cmath>

#include <iostream>

#include <string>

#include <iomanip>

// declare a constant variable M_PI and its value

double MPI = 3.14159;

using namespace std;

// Method to find the square root

double my_sqrt_1(double n)

{

   double lower_bound,upper_bound,mid_point;

   if (n < 1)

   {

       lower_bound=n;

   }

   else

   {

       lower_bound =(1+(n-1))/((2-pow((n-1),2))/8);

       upper_bound =(n+1)/2;

   }

   for (int i = 0; i < 10; ++i)

   {

       mid_point=(upper_bound+lower_bound)/2;

       if((pow(mid_point,2))>n)

           upper_bound=mid_point;

       if((pow(mid_point,2))<n)

           lower_bound=mid_point;

   }

   return mid_point;

}

// Main method

int main()

{

   double n;

   for(auto k: {-100, -10, -1, 0, 1, 10, 100})

   {

       n = MPI*pow(10.0, k);

       cout << n << " ," << sqrt(n) << " ," << my_sqrt_1(n) << '\n';

   }

}