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


double f(double x){  						// given function
	double y;
	y = (x+1.0)*(x-2.0)*(x-10.0);
	// y = sqrt(x) - tan(x);
	return y;
}

int main(){
	double xleft, xright, xmiddle;
	double yleft, yright, ymiddle;
	double accuracy;
	int i=1;

	// loop for reading data
	// will loop until valid data is entered or user-cancelled
	// i=1: read data (no or invalid data entered), i=0: cancel calculation, i=2: valid data entered

	while(i == 1){
		printf("Left bound? = ");
		scanf("%le",&xleft);
		printf("Right bound? = ");
		scanf("%le",&xright);
		printf("Accuracy? = ");
		scanf("%le",&accuracy);

		yleft = f(xleft);
		yright = f(xright);

		if(yleft*yright > 0){				// check for root between bounds - if no found, cancel calculation and ask for re-enter data
			printf("#################\n");
			printf("Invalid bounds! (no root between bounds?)\n");
			printf("Re-enter values? (0 - no, 1 - yes) ");
			scanf("%d",&i);
		}
		else{						// abort loop
			xmiddle = xleft;
			ymiddle = f(yleft);
			i=2;
		}
	}

	if(i==2){						// calculate root if valid data is entered
		while(fabs(ymiddle) > accuracy){
			xmiddle = 0.5*(xright+xleft);		// middle of the intervall [xleft,xright]
			ymiddle = f(xmiddle);
			if((ymiddle*yleft) > 0){		// set left bound to middle if sign changes in the right half of the interval
				xleft = xmiddle;
				yleft = ymiddle;
			}else{  				// set right bound to middle if sign changes in the left half of the interval
				xright = xmiddle;
				yright = ymiddle;
			}
			printf("xl: %le\txr: %le\tymid: %le\twidth: %le\n",xleft,xright,ymiddle,(xright-xleft));
		}
		printf("------------------------------------------\n");
		printf("Root found at %.15le with accuracy of %.10le\n",xmiddle,ymiddle);
	}
	return(0);
}