/* Problem 10.* Comparing Floats
Write a program that safely compares floating-point numbers (double) with precision eps = 0.000001. Note that
we cannot directly compare two floating-point numbers a and b by a==b because of the nature of the floating-point
arithmetic. Therefore, we assume two numbers are equal if they are more closely to each other than a fixed
constant eps. Examples:
 
Number a Number b Equal (with precision eps=0.000001) Explanation
5.3 6.01 false The difference of 0.71 is too big (> eps)
5.00000001 5.00000003 true The difference 0.00000002 < eps
5.00000005 5.00000001 true The difference 0.00000004 < eps
-0.0000007 0.00000007 true The difference 0.00000077 < eps
-4.999999 -4.999998 false Border case. The difference 0.000001 == eps.
We consider the numbers are different.
4.999999 4.999998 false Border case. The difference 0.000001 == eps.
We consider the numbers are different.
        */    
 
           #include <stdio.h>
 
			int compareFloats(float a, float b) {
 
				float eps = 0.000001;
				float diff;
 
				if (a > b)
					diff = a - b;
				else
					diff = b - a;
 
				printf("Floats %f and %f are ", a, b);
				if (diff >= eps)
					printf("not");
				printf(" equal (with precision eps=0.000001) ");
				}
 
            int main(void) {
 
    			compareFloats(5.3,6.01);
    			compareFloats(5.00000001,5.00000003);
    			compareFloats(5.00000005,5.00000001);
    			compareFloats(-0.0000007,0.00000007);
    			compareFloats(-4.999999,-4.999998);
    			compareFloats(4.999999,4.999998);
 
        		return 0;
            }

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