ex4.c

/* 
 * 4. Modify Program 7.8 so that the value of guess is printed each time
 * through the while loop. Notice how quickly the value of guess converges to
 * the square root. What conclusions can you reach about the number of
 * iterations through the loop, the number whose square root is being
 * calculated, and the value of the initial guess?
 *
 * By Faisal Saadatmand
 */

/*
 * Answer: The greater the number whose square root is being take, the greater
 * the initial guess, and thus, the more iteration through loop it would take
 * to approach the value of epsilon.
 */

#include <stdio.h>

/* Function to calculate the absolute value of a number */
float absoluteValue(float x)
{
	if (x < 0)
		x = -x;

	return x;
}

/* Function to compute the square root of a number */
float squareRoot(float x, const float epsilon)
{
	float guess = 1.0;

	while (absoluteValue(guess * guess - x) >= epsilon) {
		guess = (x / guess + guess) / 2.0;
		printf("%f\n", guess);
	}

	return guess;
}

int main (void) 
{
	const float epsilon = .00001;
	printf("squareRoot(2.0) = %f\n", squareRoot(2.0, epsilon));
	printf("squareRoot(144.0) = %f\n", squareRoot(144.0, epsilon));
	printf("squareRoot(17.5) = %f\n", squareRoot(17.5, epsilon));

	return 0;
}