Scale numbers to be <= 255?

Question

I have cells for whom the numeric value can be anything between 0 and Integer.MAX_VALUE. I would like to color code these cells correspondingly.

If the val

Answer 1

The "fairest" linear scaling is actually done like this:

floor(256 * value / (Integer.MAX_VALUE + 1))

Note that this is just pseudocode and assumes floating-point calculations.

If we assume that Integer.MAX_VALUE + 1 is 2^31, and that / will give us integer division, then it simplifies to

value / 8388608

Why other answers are wrong

Some answers (as well as the question itself) suggsted a variation of (255 * value / Integer.MAX_VALUE). Presumably this has to be converted to an integer, either using round() or floor().

If using floor(), the only value that produces 255 is Integer.MAX_VALUE itself. This distribution is uneven.

If using round(), 0 and 255 will each get hit half as many times as 1-254. Also uneven.

Using the scaling method I mention above, no such problem occurs.

Non-linear methods

If you want to use logs, try this:

255 * log(value + 1) / log(Integer.MAX_VALUE + 1)

You could also just take the square root of the value (this wouldn't go all the way to 255, but you could scale it up if you wanted to).