/* Compute pi by calculating the sum of areas under a quarter unit circle of
 * rectangles whose top-left corners intersect the circle.
 *
 * To compile: gcc -Wall -o pi pi.c
 *
 * To run: ./pi
 *
 * How to Change # of Threads: export OMP_NUM_THREADS= <insert number>
 *
 * Authors:
 *   Aaron Weeden, Shodor Education Foundation, 2015
 *	 Vincent X., Shodor, 2015
 */

/* We want to use the printf function to display the final result */
#include <stdio.h>

/* We want to use the sqrt function to calculate square roots */
#include <math.h>
#include <omp.h>

/* We want to make the number of rectangles constant for this run of the
 * program, and we want to declare it here so it is easier to find and change
 * later */
const int NumRectangles = 10000;

/* Every C program starts with main() */
int main() {

  /* We want a variable for the width of each rectangle. The total width is 1
   * because we are working with a quarter unit circle. */
  float width = 1.0 / NumRectangles;

  /* We want a variable for the x-coordinate at which each rectangle intersects
   * the unit circle */
  float x;

  /* We want a variable for the height of each rectangle */
  float height;

  /* We want a variable to keep a running total of the area of the rectangles */
  float area = 0.0;

  /* We want a variable for the computed value of pi */
  float pi;

  /* We want a variable to loop through the rectangles */
  int i;

  /* We want to loop over each of the rectangles and run the same code for
   * each */
   #pragma omp parallel for private(x, height) reduction(+:area)
  for (i = 0; i < NumRectangles; i++) {
  /*printf("My thread ID is %d iteration is %d\n", omp_get_thread_num(),i);*/

    /* We want to calculate the x-coordinate where the rectangle intersects the
     * circle by counting how many rectangle widths the rectangle is away from
     * the origin */
    x = i * width;

    /* We want to use the x^2 + y^2 = r^2 equation to calculate the height of
     * the rectangle, which is where the rectangle intersects the circle (y).
     * Because the circle is a unit circle, r = 1. */
    height = sqrt(1.0 - x * x);

    /* We want to compute the area of the rectangle and add it to our running
     * total */
     
    area += width * height;
     	
  }
  

  /* We are ready to compute pi. We need to multiply by 4 because we have found
   * the area under only 1/4 of the unit circle. We don't need to multiply by
   * radius squared, because the unit circle has a radius of 1. */
  pi = 4.0 * area;

  /* We want to print the final result */
  printf("%f\n", pi);

  /* We want to indicate the program has finished successfully using the Unix
   * standard value for success */
  return 0;
}