public class SqrtDemo {
	public static void main(String[] args){
		//System.out.println(ourSqrt1(75,8,9));
		System.out.println(ourSqrt2(75,8));
		System.out.println(getSinDeriv(1));
		
	}
	// look for sqrt(x) between lower and upper bounds
	public static float ourSqrt1(float x, float lower, float upper){
		if(lower*lower > x){
			throw new IllegalArgumentException("lower is too large");
		}
		else if (upper*upper < x){
			throw new IllegalArgumentException("upper is too small");
		}
		float mid = 0;
		while(true){
			mid = (lower + upper)/2;
			// quit if cannot make any further improvement
			// because lower and upper are consecutive floats
			if(mid == lower|mid == upper){
				break;
			}
			System.out.println(""+lower+" "+ upper+" "+  mid);
			float midsq = mid*mid;
			if(midsq < x){ //search to right
				lower = mid;
			}
			else if(midsq > x){//search to left
				upper = mid;
			}
		} 
		return mid;
	}
	// this method converges much faster
	public static double ourSqrt2(double x, double init){
		double s = init;
		while(true){
			// think of s and xos as being two sides of a 
			// rectangle whose area is s*xos = x
			// we want the rectangle to be "more square"
			// so we set the new x to their average
			double xos = x/s;
			double diff = Math.abs(xos - s);
			if(diff < 1e-14){
				break;
			}
			s = (s + xos)/2;
			System.out.println(""  + s + " " + diff);
		}
		return s;
	}
	// this illustrates cancellation
	public static double getSinDeriv(double x){
		// suppose we have Math.sin but not cos
		double h = 1;
		double divDif = 0;
		for(int j=0;j<20;j++){
			h = h/10;

			double d1 = Math.sin(x + h);
			double d2 = Math.sin(x);
			divDif = (d1 - d2)/h;
			System.out.println("" + d1 + d2 + divDif + " " + h);
		}
		System.out.println("right answer is"+ Math.cos(x));
		return divDif;
	}

}