#include <stdio.h>
#include <unistd.h>
#include <sys/time.h>
#include <math.h>


#define TIMER_CLEAR     (tv1.tv_sec = tv1.tv_usec = tv2.tv_sec = tv2.tv_usec = 0)
#define TIMER_START     gettimeofday(&tv1, (struct timezone*)0)
#define TIMER_ELAPSED   (double) (tv2.tv_usec-tv1.tv_usec)/1000000.0+(tv2.tv_sec-tv1.tv_sec)
#define TIMER_STOP      gettimeofday(&tv2, (struct timezone*)0)
struct timeval tv1,tv2;

double func(double num)
{
    return sqrt(1-pow(num,2));
}

int main(int argc, char * argv[])
{
    TIMER_CLEAR;
    if (argc < 2)
	{
		printf("Please specify the iterations\n");
		return -1;
	}
	
    float iterations = atoi(argv[1]);
    // integral bounds
    float integral, sumOfRectangles;
    double a,b, area;
    a=0;
    b=1;
    double h = (b-a)/iterations;
    int i=0;
    TIMER_START;
    // sum up Trapezoids
    for (i; i <= iterations-1; i++)
    {
        area=h*func(a+(i-1)*h);
        sumOfRectangles+=area;        
    }
    integral=4*sumOfRectangles;
    TIMER_STOP;
    //integral = h*((sqrt(1-pow(a,2))/2)+sumOfTrapezoids+sqrt(1-pow(a,2))/2);
    printf("Computed Sum for Rectangular Decomposition: %f\n", integral);
    printf("Time elapsed = %f seconds\n", TIMER_ELAPSED);
}