Change zoom precision function

[AntonKhorev]

This changes the number of fractional digits to log10(pixels / degrees) with pixels = 2**(8 + zoom) and degrees = 180.

---

If you apply the entire #5064, zoom in to the max zoom level, place an endpoint marker and try to drag it around, you'll notice it moves by jumping several pixels. This is because I limit its coordinates to zoom precision and zoom precision is not high enough. Its current version was introduced in b28511f. You can notice something strange about it: the zoom value went from being an argument of Math.pow to an argument of Math.log. zoom is already on a log scale, why do you need to take its log again?

zoom	old zoomPrecision	new zoomPrecision
0	0	1
1	0	1
2	1	1
3	2	2
4	2	2
5	3	2
6	3	2
7	3	3
8	3	3
9	4	3
10	4	4
11	4	4
12	4	4
13	4	5
14	4	5
15	4	5
16	4	5
17	5	6
18	5	6
19	5	6
20	5	7
21	5	7

Some layers go up to zoom 21, precision limits become very noticeable there. Even on level 0 you need at least one digit after . to translate -90..+90 to 256 tile pixels.

[tomhughes]

I'm not disputing there may be a problem here but it would be good to understand how you have derived the new formula you're using - the fact that the output repeats some values 3 times and some 4 times seems a little to me and suggests that the formula is slightly off somewhere causing rounding issues?

[AntonKhorev]

ceil( log10(2**(8+zoom) / 180) )

2**(8+zoom) = world size in pixels
180 = span of latitude values
2**(8+zoom) / 180 = number of pixels in one degree. If there are 100 pixels in one degree, you need log10(100) = 2 fractional digits to represent a degree value for a given pixel offset

[AntonKhorev]

repeats some values 3 times and some 4

Because numbers are base-ten not base-some-power-of-2 and zoom levels magnify by powers of 2. On average numbers are repeated log2(10) times.

[tomhughes]

ceil( log10(2**(8+zoom) / 180) )

Would it not be better just to use that then? Yes I can prove using logarthmic identities that what you've written is the same but it's not clear why you prefer the transformed version?

I also suspect the Math.max is no longer needed as it can't go negative for any sane zoom - it was needed before because log10 breaks down for zoom zero...

[AntonKhorev]

If you don't mind raising something to a variable power* and taking a logarithm of the result, here's a more readable version.

* could have used pixels = 1 << (8 + zoom), not sure if it's more clear

[tomhughes]

Thanks. I think that makes it a lot clearer what is going on for future maintainer.