Question

I’m not sure if this can be done without some determining factor….but wanted to see if someone knew of a way to do this.

I want to create a shifting scale for numbers.

Let’s say I have the number 26000. I want the outcome of this algorithm to be 6500; or 25% of the original number. But if I have the number 5000, I want the outcome to be 2500; or 50% of the original number.

The percentages don’t have to be exact, this is just an example.

I just want to have like a sine wave sort of thing. As the input number gets higher, the output number is a lower percentage of the input.

Does that make sense?

Answer 1

Something like f(x) = x / log x?

x         | f(x)
=======================
26000     | 5889 (22.6 %)
5000      | 1351 (27.2 %)
100000    | 20000 (20 %)
1000000   | 166666 (16.6 %)

Just a simple example. You can tweak it by playing with the base of the logarithm, by adding multiplicative constants on the numerator (x) or denominator (log x), by using square roots, squaring (or taking the root of) log x or x etc.

Here’s what f(x) = 2*log(x)^2*sqrt(x) gives:

x         | f(x)
=======================
26000     | 6285 (24 %)
5000      | 1934 (38 %)
500       | 325 (65 %)
100       | 80 (80 %)
1000000   | 72000 (7.2 %)
100000    | 15811 (15 %)