CPUMeter: Improve spacing between sub-meter algorithm

[Explorer09]

Fixes #1654. The formula is derived by myself.

Interestingly, I asked both ChatGPT and Google Gemini (AI) on how to make a formula based on a table of given values, they either gave me a wrong result or simply fail to make one. (I don't trust these AIs in general, by the way.) (https://chatgpt.com/share/67e6fb4a-da80-8004-a993-11cc19666fad) (https://g.co/gemini/share/356fa79d2f5a)

[Explorer09]

Please explain those magic numbers …

It's a bit difficult to explain in code. I wonder if you or other people have ideas to make the code more readable (maybe wrap it into a function or something - I don't know how to name such function, though).

Anyway. Here're my explanations:

1. The goal is to make the sub-meters of each CPU core/thread aligned despite the number of sub-columns of a CPU meter (group).
2. Currently, there can only be 2, 4 or 8 sub-columns for a meter.
3. The idea is to adjust the distribution of "spaces" between sub-meters based on the remainder of (w mod ncol). Since the width of each sub-meter is floor(w / ncol), the total number of spaces to distribute would be equal to (w mod ncol).
4. When the remainder is a multiple of 2, there should not be a space inserted in the (ncol / 2) position or otherwise this meter (group) would appear misaligned with other meter groups with 2 sub-columns.
5. Apply the similar rule: When the remainder is a multiple of N, there should not be a space inserted in the (ncol * M / N) position (where M is any integer in the range [1, N-1]) or otherwise this meter (group) would appear misaligned with other meter groups with N sub-columns.
6. The problem may be more complicated if N can be any positive integer (it would require integer factorisation and a loop), so I narrow the problem scope to cases where N is a power of two, like 2, 4, 8, 16 and 32.
7. Pseudocode: (EDIT: this pseudocode is inaccurate in describing the actual algorithm; I will correct it later.)

spacing_function(ncol, i, w) {
   // 'i' is column index of the sub-meter.
   // assert(i >=0 && i < ncol);
   w %= ncol;
   res = 0;
   foreach (N in {2, 4, 8, 16, 32}) {
      if ((w + 1) % N == 0)
         res += (int)(i * N / ncol);
   }
   return res;
}

It technically requires a loop. So I use bit manipulation tricks to simplify this, utilising N is a power of two within the narrowed problem scope, and came up with the magic numbers for multiplication and mask values.

((w % ncol) * 32 / ncol) // Maximum number of columns is 32 for this formula. (v * 0x00210842U) & 0x02082082U) // Break the remainder of (w % ncol) into 5 separate bits, and reverse the bit order. ... * (unsigned int)(i / nrows) // Make up to 5 copies of this column index value, but if ((w + 1) % N != 0) set that copy to zero. (v + 0x02108420U) & 0x7DE71840U) // Compute the addends that's equivalent to the (int)(i * N / ncol) in the pseudocode, for each copy. (... * 0x00210842ULL) >> 27 // Sum up all 5 numbers for the final result.

Before
w=56 | [99.5%][99.5%][99.5%][99.5%][99.5%][99.5%][99.5%][99.5%]
w=57 | [99.5%] [99.5%][99.5%][99.5%][99.5%][99.5%][99.5%][99.5%]
w=58 | [99.5%] [99.5%] [99.5%][99.5%][99.5%][99.5%][99.5%][99.5%]
w=59 | [99.5%] [99.5%] [99.5%] [99.5%][99.5%][99.5%][99.5%][99.5%]
w=60 | [99.5%] [99.5%] [99.5%] [99.5%] [99.5%][99.5%][99.5%][99.5%]
w=61 | [99.5%] [99.5%] [99.5%] [99.5%] [99.5%] [99.5%][99.5%][99.5%]
w=62 | [99.5%] [99.5%] [99.5%] [99.5%] [99.5%] [99.5%] [99.5%][99.5%]
w=63 | [99.5%] [99.5%] [99.5%] [99.5%] [99.5%] [99.5%] [99.5%] [99.5%]
w=64 | [|99.5%][|99.5%][|99.5%][|99.5%][|99.5%][|99.5%][|99.5%][|99.5%]
w=65 | [|99.5%] [|99.5%][|99.5%][|99.5%][|99.5%][|99.5%][|99.5%][|99.5%]
w=66 | [|99.5%] [|99.5%] [|99.5%][|99.5%][|99.5%][|99.5%][|99.5%][|99.5%]
w=67 | [|99.5%] [|99.5%] [|99.5%] [|99.5%][|99.5%][|99.5%][|99.5%][|99.5%]
w=68 | [|99.5%] [|99.5%] [|99.5%] [|99.5%] [|99.5%][|99.5%][|99.5%][|99.5%]
w=69 | [|99.5%] [|99.5%] [|99.5%] [|99.5%] [|99.5%] [|99.5%][|99.5%][|99.5%]
w=70 | [|99.5%] [|99.5%] [|99.5%] [|99.5%] [|99.5%] [|99.5%] [|99.5%][|99.5%]
w=71 | [|99.5%] [|99.5%] [|99.5%] [|99.5%] [|99.5%] [|99.5%] [|99.5%] [|99.5%]
w=72 | [||99.5%][||99.5%][||99.5%][||99.5%][||99.5%][||99.5%][||99.5%][||99.5%]

After
w=56 | [99.5%][99.5%][99.5%][99.5%][99.5%][99.5%][99.5%][99.5%]
w=57 | [99.5%][99.5%][99.5%][99.5%] [99.5%][99.5%][99.5%][99.5%]
w=58 | [99.5%][99.5%] [99.5%][99.5%][99.5%][99.5%] [99.5%][99.5%]
w=59 | [99.5%][99.5%] [99.5%][99.5%] [99.5%][99.5%] [99.5%][99.5%]
w=60 | [99.5%] [99.5%][99.5%] [99.5%][99.5%] [99.5%][99.5%] [99.5%]
w=61 | [99.5%] [99.5%][99.5%] [99.5%] [99.5%] [99.5%][99.5%] [99.5%]
w=62 | [99.5%] [99.5%] [99.5%] [99.5%][99.5%] [99.5%] [99.5%] [99.5%]
w=63 | [99.5%] [99.5%] [99.5%] [99.5%] [99.5%] [99.5%] [99.5%] [99.5%]
w=64 | [|99.5%][|99.5%][|99.5%][|99.5%][|99.5%][|99.5%][|99.5%][|99.5%]
w=65 | [|99.5%][|99.5%][|99.5%][|99.5%] [|99.5%][|99.5%][|99.5%][|99.5%]
w=66 | [|99.5%][|99.5%] [|99.5%][|99.5%][|99.5%][|99.5%] [|99.5%][|99.5%]
w=67 | [|99.5%][|99.5%] [|99.5%][|99.5%] [|99.5%][|99.5%] [|99.5%][|99.5%]
w=68 | [|99.5%] [|99.5%][|99.5%] [|99.5%][|99.5%] [|99.5%][|99.5%] [|99.5%]
w=69 | [|99.5%] [|99.5%][|99.5%] [|99.5%] [|99.5%] [|99.5%][|99.5%] [|99.5%]
w=70 | [|99.5%] [|99.5%] [|99.5%] [|99.5%][|99.5%] [|99.5%] [|99.5%] [|99.5%]
w=71 | [|99.5%] [|99.5%] [|99.5%] [|99.5%] [|99.5%] [|99.5%] [|99.5%] [|99.5%]
w=72 | [||99.5%][||99.5%][||99.5%][||99.5%][||99.5%][||99.5%][||99.5%][||99.5%]