Programming Resources For Fun and Learning

RoundoffError

 Output.txt RoundoffError.java

RoundoffError.java

```public class RoundoffError {
public static void main(String[] args) {
float x = 1.0f;
float y1 = 0.00000005f;
float y2 = 0.00000006f;

System.out.println("Adding a small number to 1");
float z=x+y1;
System.out.printf("%1.9f + %1.9f  = %1.9f\n",x, y1, z);
z=x+y2;
System.out.printf("%1.9f + %1.9f  = %1.9f\n\n",x, y2, z);

System.out.println("Adding a small number to 1 a bunch of times");
z = x;
int n = 10000;
for(int i=0;i<n;i++) {
z = z + y1;
}
System.out.printf("%1.9f + %1.9f*%d  = %1.9f\n",x, y1, n, z);

z = x;
n = 10000;
for(int i=0;i<n;i++) {
z = z + y2;
}
System.out.printf("%1.9f + %1.9f*%d  = %1.9f\n\n",x, y2, n, z);

System.out.println("Adding a multiple of a small number to 1");
z = x + y1*n;
System.out.printf("%1.9f + %1.9f*%d  = %1.9f\n",x, y1, n, z);
z = x + y2*n;
System.out.printf("%1.9f + %1.9f*%d  = %1.9f\n\n",x, y2, n, z);

System.out.println("(a-b)^2 == a*a - 2*a*b + b*b ?");
float a = 1;
float b = 0.0000005f;
float c = (a-b);
float cs1 = c*c;
float cs2 = a*a - 2*a*b + b*b;

System.out.printf("(%1.9f - %1.9f)^2 = (%1.9f)^2  = %1.9f\n",a, b, c, cs1);
System.out.printf("(%1.9f - %1.9f)^2  = %1.9f\n",a, b, cs2);

if(cs1==cs2) {
System.out.println("They are the equal");
} else {
System.out.println("They are the not equal");
}
}
}
```