// name: Devin Scott N23 CS407
// Assignment A02

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


int signof(double x)
{
if (x >= 0)
return 1;

else 
return 0;

}

double compute_poly(double x)
{
	double result=0;
	//result=x;

	printf("\n  passed value of x was... %f \n", x);
	
	
	result = result + (pow(x, 4));
	//printf("\n  computing result... %f \n", result);
	result = result + (4 * (pow(x,3)) );
	//printf("\n  computing result... %f \n", result);
	result = result - (4 * (pow(x,2)) );
	//printf("\n  computing result... %f \n", result);
	result = result - (16*x);
	//printf("\n  computing result... %f \n", result);
	result = result - 8;
	//printf("\n  computing result... %f \n", result);

	


	return result;
}
int main ()
{
	int max_iterations=0;
	int num_subintervals=0;
	double relative_err=0;
	double lower_limit=0;
	double upper_limit=0;
	double temp=0.0;
	double tempx=0.0;
	double low_interval = -1.0;
	double high_interval = 0.0;
	double trial_range=0.0;
	double sub_interval=0.0;
	double temp_interval=0.0;
	double lower_value=0.0;
	double upper_value=0.0;
	double lower_secant_interval=0;
	double upper_secant_interval=0;
	int i=0;

	printf ("\n Devin Scott NN: 23 Numerical Analysis\n");  //header

														//collect input from user
														//input is "lower limit","upper limit"
														//"number of subintervals","relative error thresh",
														//"maximum number of iterations"

	printf ("\n please enter the lower limit \n");
	scanf("%lf",&lower_limit); 
	printf ("\n please enter the upper limit \n");
	scanf("%lf",&upper_limit); 
	printf ("\n please enter the  number of sub-intervals\n");
	scanf("%d",&num_subintervals); 
	printf ("\n please enter the relative error threshold  \n");
	scanf("%lf",&relative_err); 
	printf ("\n please enter the maximum number of iterations \n");
	scanf("%d",&max_iterations); 

	printf("\n .. lower limit was %e \n",lower_limit);
	printf("\n .. upper limit was %e \n",upper_limit);
	printf("\n .. number of sub intervals was %d \n",num_subintervals);
	printf("\n .. relative error threshold was %e \n",relative_err);
	printf("\n .. max iterations was %d \n",max_iterations);
	printf("\n .. range of trial interval is from %f to %f \n", lower_limit, upper_limit);
	trial_range = abs(( (abs(lower_limit)) - (abs(upper_limit)) ));
	printf("\n .. total absolute range of trial interval is %f \n", trial_range);
	sub_interval=(trial_range/num_subintervals);
	printf("\n .. range of each sub-interval is %f \n", sub_interval);

	temp_interval=lower_limit;
	for (i=0; i<num_subintervals; i++)
	{
		printf("\n ..testing sub-interval from %f \n", temp_interval);
		lower_value = compute_poly(temp_interval);
		
		temp_interval = temp_interval+sub_interval;
		printf("\n ..to .. %f \n", temp_interval);
		upper_value = compute_poly(temp_interval);
		
		printf("\n lower value was  %f \n", lower_value);
		printf("\n  upper value was  %f \n", upper_value);
		
		if ( signof(lower_value) == signof(upper_value) )
		{	printf("\n the signs were the same. no root! \n");
			
	
		}
		else
		{
			
			lower_secant_interval=(temp_interval-sub_interval);
			upper_secant_interval=(temp_interval);
			printf("\n sign change detected in the sub-interval %f to %f ", lower_secant_interval, upper_secant_interval  );
		}

	}

	

	/*

	printf("\n .. polynomial is x^4 + 4x^3 - 4x^2 - 16x - 8 \n  please enter a value x to compute");
    scanf("%lf",&tempx);
	printf("\n  the x was %f \n", tempx);
	temp = compute_poly(tempx);
	printf("\n  the result was %f \n", temp);
	
	*/
	
	
	return 0;
}