Question

What to do

Write a C program that computes Pi with the approximation algorithm that I introduced in class. I want you to write the program in two different ways:

• The first version will add up the first 28284277 elements of the approximation series in a simple for loop. I ask you to put the code into a function with this signature: float get_pi_for(void);
• The second version will break out of a while loop depending on whether a pair of adjacent elements (remember that we always consider a positive element and its adjacent negative right neighbor) is smaller than a certain threshold. I ask you to use the threshold 0.00000000000001. Please put the code of this version into a function with the signature float get_pi_while(void);

Put both functions into a file called pi.c. Also write a corresponding header file that has symbolic constants for both the number of LOOPS to be run as well as for the THRESHOLD value.

Finally, write a file main.c that contains the driver, which will print out pi twice calling the two different functions. I want you to call get_pi_for() first, then call  get_pi_while().

What to submit

• All three code files
• A screen shot of a run of your driver with the exact numbers for LOOPS and THRESHOLD given above

//pi.h

# define threshold 0.00000000000001
float get_pi_for();
float get_pi_while();

//pi.c

# include <stdlib.h>
# include <stdio.h>
# include <limits.h>

#include"pi.h"

//# define threshold 0.00000000000001

float get_pi_for()

{
   double pi = 0;
unsigned long index = 1;

double temp = 0;

while (temp - threshold)
{

temp += ((4.0/index) - (4.0/index+2));

index += 4;
}
pi = temp;
return pi;
}

float get_pi_while()
{
   double pi = 0;
unsigned long index = 1;

int sign = 1;

while (index < 28284277)
{

pi += 4.0/index * sign;
sign *= -1;
index += 2;
}
return pi;
}

//main.c

#include"pi.c"
#include"pi.h"

int main()

{
   printf("Value of pi using for loop is %f\n",get_pi_for());
   printf("Value of pi using while loop is %f\n",get_pi_while());
   return EXIT_SUCCESS;
}

Answer 1

// pi.h

#ifndef PI_H_

#define PI_H_

# define THRESHOLD 0.00000000000001

# define LOOPS 28284277

float get_pi_for();

float get_pi_while();

#endif /* PI_H_ */

//end of pi.h

// pi.c

#include "pi.h"

float get_pi_for()

{

               float pi = 0;

               int index = 1;

               int sign = 1;

               for(int i=0;i<LOOPS;i++)

               {

                              pi += sign*4*(((float)1)/index);

                              sign = -1*sign;

                              index += 2;

               }

               return pi;

}

float get_pi_while()

{

               float curr_pi = 4, prev_pi = 0;

               int index=3;

               int sign = -1;

               float eps = curr_pi-prev_pi;

               if(eps < 0)

                              eps = -1*eps;

               while(eps > THRESHOLD)

               {

                              prev_pi = curr_pi;

                              curr_pi += sign*4*(((float)1)/index);

                              eps = curr_pi-prev_pi;

                              if(eps < 0)

                                             eps = -1*eps;

                              index += 2;

                              sign = -1*sign;

               }

               return curr_pi;

}

//end of pi.c

// main.c

#include "pi.h"

# include <stdlib.h>

# include <stdio.h>

int main()

{

               printf("Value of pi using for loop is %f\n",get_pi_for());

               printf("Value of pi using while loop is %f\n",get_pi_while());

               return EXIT_SUCCESS;

}

//end of main.c

Output: