Rounding Y To Make Mod(x,y) = 0

[AliMoradi]

I have two variables, X and Y. X is some value that cannot be changed and Y is some random value less than 1 (most likely an irrational number as well) that cannot increase. I'm trying to figure out a way to round Y down, so as to make (X % Y = 0).

For example, if x = 2 and y = 0.0137, then x/y = 145.9854015~. Now to make x % y = 0, I have to round 0.0137 down to the nearest decimal that will do so, which would be Y = 0.0125.

I've come up with a few ways of doing this, but none of them work for all cases (for any x and y). Do you guys have any suggestions as to how I can tackle this?

Thanks in advance for any help!

- Ali

[Telion]

Divide X by an integer, starting with 1. If the result is lower than Y, set Y to the result. Otherwise, add 1 to X and try again.

[AliMoradi]

So what you're saying is that I do this?

double x = 2;
double xx;
double y = 0.0137;
int G = 0;
int S = 1;
while (G == 0)
{
    xx = x/S;
    if (xx < y)
    {
        y = xx;
        G = 1;
    }
    else
    {
        S = S + 1;
    }
}

But how does that make the modulus = 0? I think I may have misunderstood you.

[Telion]

If the algorithm works as I suspect, it will always result in a modulus of 0 (at least for reasonable, valid inputs).

A modulus of 0 really means that x is some multiple of Y. After the loop, y contains x / xx, so y = xx * x, making y a multiple of x. Moreover, this algorithm starts by dividing by 1, getting results in decreasing order until the result is less than y, so y will always be set to the valid result just below its previous value; it never rounds up.


In your case, x is 2 and y is 0.0137. The program will divide by 1, see that the result is 2 which is greater than 0.0137, and try again. Then it will divide by 2, see that the result is 1 which is greater than 0.0137, and try again. This will keep going until it reaches 146. 2.0 / 146 is just below 0.0137, and y will be reduced to that value. After that, x mod y should be as close as is reasonably possible to 0.

[AliMoradi]

The issue is that the algorithm will usually generate irrational or rational but repeated numbers. For example, when running that algorithm for x = 2, y = 0.0137, it generates a y value of 0.013698630136986 (calculation done in MATLAB for this one example). Is there any way to do this so that it doesn't generate irrational or repeating numbers?