/* Name: Garrett Haldrup
pi.c
Problem: Experiments with different methods of calculating pi, and sees how close they get to the real thing 
Certification of Authenticity:
I certify that this assignment is entirely my own work.
*/

#include <stdio.h>
#include <math.h>

double piWallis(int n);
double piGregory(int n);
double piNilakantha(int n);
double piEuler(int n);
void piCompare(double pi);


int main() {

  int n;
  double pi;

  printf("Enter the number of n iterations to do\nfor each method of calculating pi: ");
  scanf("%d", &n);

  pi = piWallis(n);
  piCompare(pi);
  pi = piGregory(n);
  piCompare(pi);
  pi = piNilakantha(n);
  piCompare(pi);
  pi = piEuler(n);
  piCompare(pi);
}

double piWallis(int n) {
  int top = 0;
  int bottom = 1;
  double pi = 1;

  printf("\nThis will calculate pi using the Wallis Method.\n");

  for (int i = 0; i < n; i++) {
    top += ((i + 1) % 2) * 2;
    bottom +=  (i % 2) * 2;
    pi *= (float)top / (float)bottom;
  }
  pi *= 2;
  printf("The %d of pi is: %lf\n",n ,pi);
  return pi;
}

double piGregory(int n) {
  int top = 4;
  int bottom = 1;
  double pi = 0;

  printf("\nThis will calculate pi using the Gregory Method.\n");

  for (int i = 0; i < n; i++) {
    bottom = (1 + (2 * i))  * pow(-1, i);
    pi += (float)top / (float)bottom;
  }
  printf("The %d of pi is: %lf\n",n ,pi);
  return pi;
}

double piNilakantha(int n) {
  int top = 4;
  int bottom;
  double pi = 3;

  printf("\nThis will calculate pi using the Nilakantha Method.\n");

  for (int i = 1; i < n; i++) {
    bottom = (2*i) * (2*i+1) * (2*i+2) * pow(-1, i - 1);
    pi += (float)top / (float) bottom;
  }

  printf("The %d of pi is: %lf\n",n ,pi);
  return pi;
}

double piEuler(int n) {
  int bottom;
  double pi = 0;

  printf("\nThis will calculate pi using the Euler Method.\n");

  for (int i = 0; i < n; i++) {
    bottom = pow(i+1,2);
    pi += 1.0 / bottom;
  }
  pi = sqrt(6 * pi);
  printf("The %d of pi is: %lf\n",n ,pi);
  return pi;
}

void piCompare(double pi) {
  double diff;

  diff = M_PI - pi;
  printf("The difference from the actual value of pi is: %lf\n", diff);
}