Question

I have two

double a, b;

I know that the following is true

-1 <= a/b <= 1

however b can be arbitrarily small. When I do this naively and just compute the value

 a/b

the condition specified above does not hold in some cases and I get values like much greater than 1 in absolute value (like 13 or 14.)

How can I ensure that when I divide by b, I get a value such that the condition mentioned above can be enforced. In the case where I can not guarantee this I am happy to set the computed value a/b to 0.

Answer 1

What you need to enforce is abs(a)≤abs(b). If that condition holds, then -1≤a/b≤1, regardless of floating-point precision used. Your logic error is occurring before the division, since at the division point abs(a)>abs(b) which violates your a-priori requirement.