I was wondering how to set a weight for a computation of huge different values. I will try to explain it better, or maybe in details.
The idea is: I would like to have as a result a value in this range [1,20] given: 1) first value: a 1a) with a format like 0.1 or 0.0001 or 0.00001 etc. 1b) maximum decimal length = 5 decimals 2) second value: b 2a) assumption that is less than a (if a=0.01, at least b=0.00999 etc.) 2b) with the same format 2c) maximum decimal length = 6 decimals (so 1 grater than a)
where, given for example a=0.01 and b=0.0001
x = a/b = 100
a second example a=0.01 and b=0.00001
x = a/b = 1000
I thought at something like this: If maximum could be (when a=0.1 and b=0.000001) = 100000 than it correspond to 20 (the new maximum scale) and if I count the difference of number of decimals I can say that: 'a' has 1 decimal 'b' has 6 decimal In general we can have a maximum difference of 5, so:
max = 5
So using this calculus:
diff=6-1=5
in order to correspond their fraction (a/b) as the maximum value (20) I can do:
(diff*20)/max give me 20. That's ok.
Now, If I have a=0.1 and b=0.000002
I can use the least significant number of 'b' (in this case '2' of 0.000002) and compare with the least significant of 'a', and I can say that
diff=6-1=5
Now subtract 0.2 (because the least significant number was 2) to have 4.8. Now recompute:
4.8*20/max = 19.2
So for 0.1 and 0.000003 would be
diff=6-1=5
diff=diff-0.3 = 4.7
4.7*20/max = 18.8
And so on.
The problem is that when I have a=0.3 and b=0.0002 (for example) I don't know how to manage it.
Could anyone suggest me a solution or a bunch of that even with a pseudo-code or procedure? Maybe I will do the translation in java by myself.
I don't know where to post my question, if so I really apologize if I wrong some rules of these website, otherwise everything is fine :-) Thank you all
Have you looked at logarithms?
d = (log(a) - log(b))/log(10)
should give the answer. In other words, log(a)/log(10) gives you
0.1 --> -1
0.01 --> -2
0.001 --> -3
etc. So, you can calculate differences the way you want. And in the end,
exp(d*log(10))
is the actual ratio. In java, use Math.log()