How can I turn a floating point number into the closest fraction represented by a byte numerator and denominator?

Question

How can I write an algorithm that given a floating point number, and attempts to represent is as accurately as possible using a numerator and a denominator, both restricted

Answer 1

I would comment, but I don't have rep yet...

Eric's answer above doesn't consider the case where an exact result is possible. For example, if you use 0.4 as input, then the representation should be 2/5, in which case you end up with a division by zero in the third iteration of the loop (r=0 on second loop => r = 1/r error on third).

So you want to modify the while loop to exclude that option:

while(true)

should be

while(r != 0)