/*
 * combined.c
 *
 * This program combines what we saw before.  It calculates e and pi
 * and then integrates the x^2.  We also print out the elapsed time in
 * ms at several points in our program.  We have replaced the function y=x^2
 * with a more complex polynomial 3x^3 + 2x^2 + x.
 */

#include <stdio.h>
#include <time.h>

#define num_steps 10000000 /* steps to use in taylor expansions */
#define int_steps (1<<30)  /* steps to use in integration */

int main(int argc, char *argv[])
{
  double start, stop; /* times of beginning and end of procedure */

  /* Values for part 1 */
  double e, pi, factorial, product;
  int i;

  /* Values for part 2 */
  double sum;
  double x;

  /* start the timer */
  start = clock();

#pragma omp parallel reduction(+: sum)
  {
#pragma omp sections nowait
    {
#pragma omp section
      {
	/* First we calculate e from its taylor expansion */
	printf("e started at %.0f\n", clock()-start);
	e = 1;
	factorial = 1;
	for (i = 1; i<num_steps; i++) {
	  factorial *= i;
	  e += 1.0/factorial;
	}
	printf("e done at %.0f\n", clock()-start);
      }
#pragma omp section
      {
	/* Then we calculate pi from its taylor expansion */
	printf("pi started at %.0f\n", clock()-start);
	
	pi = 0;
	for (i = 0; i < num_steps*20; i++) {
	  pi += 1.0/(i*4.0 + 1.0);
	  pi -= 1.0/(i*4.0 + 3.0);
	}
	pi = pi * 4.0;
	printf("pi done at %.0f\n", clock()-start);
      }
    } /* sections */

    /* Now we integrate the function */
    printf("integration started at %.0f\n", clock()-start);
    sum = 0;
#pragma omp for nowait
    for (i = 0; i<int_steps; i++) {
      x = 2.0 * (double)i / (double)(int_steps); /* value of x */
      sum += ( 3*x*x*x + 2*x*x + x ) / int_steps;
    }

#pragma omp single /* we only need to print this once */
    printf("integration done at %.0f\n", clock()-start);


#pragma omp barrier
    /* make sure all threads are caught up before we do the multiplication */
    product = e * pi;
  
  } /* omp parallel */

  /* we're done so stop the timer */
  stop = clock();

  printf("Values: e*pi = %f,  integral = %f\n", product, sum);
  printf("Total elapsed time: %.3f seconds\n", (stop-start)/1000);

  return 0;
}