"normalizing" a value

[Steven D'Aprano]

On Thu, 2 Jul 2015 10:12 am, bvdp wrote:

> Not sure what this is called (and I'm sure it's not normalize). Perhaps
> "scaling"?


Could be normalising, could be scaling.
 
> Anyway, I need to convert various values ranging from around -50 to 50 to
> an 0 to 12 range (this is part of a MIDI music program). I have a number
> of places where I do:

You say "around" -50 to 50. Can you get 51? 151? How do you want to treat
such out of range numbers?

Are the values integer valued, or can they include fractional values like
27.356?

>    while x < 0: x += 12
>    while x >= 12: x -= 12
> 
> Okay, that works. Just wondering if there is an easier (or faster) way to
> accomplish this.


One approach is to just re-scale the numbers from the range -50...50 to
0...12 inclusive. That is:

    before => after
    -50 => 0
    0 => 6
    50 => 12


and everything in between is scaled equivalently. Given x between -50 and 50
inclusive, calculate:

    y = (x+50)/100.0*12


(Note that in Python 2, you need to make at least one of those values a
float, otherwise you may get unexpected results.)

That will give you y values from the range 0.0 to 12.0 inclusive. If x is
less than -50.0 or more than +50.0 y will likewise be out of range. You can
clip the result:

    y = min(12.0, max(0.0, y))

If your x values are integer values (no fractional values) between -50 and
+50 you can use clock arithmetic. Think of a clock marked 0 to 12 (so there
are 13 values), once you reach 12 adding 1 takes you back to 0.

    0, 13, 26, 39 => 0
    1, 14, 27, 40 => 1
    2, 15, 28, 41 => 2
    ...
    12, 25, 38, 51 => 12


Extending that to negative values in the most obvious fashion:

    -1, -14, -27, -40 => 12
    ...
    -12, -25, -38, -51 => 1
    -13, -26, -39, -52 => 0
    

We can do that easily with the % (modulo) operator:

    y = x % y


Modulo even works with non-integer values:

py> 13.5 % 13
0.5



-- 
Steven