Improve funkcia algorithm to avoid factorization

[exyi]

I also fixed a bug: previous implementation would return 0, if the result was supposed to be 1 as a result of modulo operation (i.e. result is 1_000_000_008, modulo result is 1, which was replaced and 0 was returned)

[Sejsel]

I am not gonna lie, I don't understand it completely, I would have to go through the math, especially towards the end of funkcia, but thank you so much for this. Looks great, just some tiny things.

[Sejsel]

I also ran a few bigger programs from my advent of code solutions (here), and it looks like there is somehow a significant perf regression on usual programs.

My first guess was that we no longer have a special case for the common inputs (a==b), but we do. Second guess was that we inline a function that is very long now, and it might have impact. But I tried to avoid that and handle special cases outside, and perf did not change. So not sure what the reason is right now, hopefully not different Rust versions used to compile it. Might try investigating more later.

I saw the same behavior on all programs, one example on the day 3 part 2 program, it was 4% slower than before (a very dumb way of testing, but I repeated it multiple times and it always was clearly slower)

# old version

❯ for x in (seq 10); ksplang --stats ksplang/3-2.ksplang --text-input < inputs/3.txt; end
Execution time: 1.214007277s
Instructions executed: 119309701 (98.3M/s)
Execution time: 1.228749622s
Instructions executed: 119309701 (97.1M/s)
Execution time: 1.203303312s
Instructions executed: 119309701 (99.2M/s)
Execution time: 1.238919269s
Instructions executed: 119309701 (96.3M/s)
Execution time: 1.230999355s
Instructions executed: 119309701 (96.9M/s)
Execution time: 1.219730683s
Instructions executed: 119309701 (97.8M/s)
Execution time: 1.233437634s
Instructions executed: 119309701 (96.7M/s)
Execution time: 1.235833891s
Instructions executed: 119309701 (96.5M/s)
Execution time: 1.233339841s
Instructions executed: 119309701 (96.7M/s)
Execution time: 1.211065025s
Instructions executed: 119309701 (98.5M/s)

# new version

❯ for x in (seq 10); ksplang/target/release/ksplang-cli --stats ksplang/3-2.ksplang --text-input < inputs/3.txt; end
Execution time: 1.275257566s
Instructions executed: 119309701 (93.6M/s)
Execution time: 1.269184171s
Instructions executed: 119309701 (94.0M/s)
Execution time: 1.249723653s
Instructions executed: 119309701 (95.5M/s)
Execution time: 1.269717628s
Instructions executed: 119309701 (94.0M/s)
Execution time: 1.292459461s
Instructions executed: 119309701 (92.3M/s)
Execution time: 1.281289692s
Instructions executed: 119309701 (93.1M/s)
Execution time: 1.297168222s
Instructions executed: 119309701 (92.0M/s)
Execution time: 1.286744218s
Instructions executed: 119309701 (92.7M/s)
Execution time: 1.262160706s
Instructions executed: 119309701 (94.5M/s)
Execution time: 1.273051297s
Instructions executed: 119309701 (93.7M/s)

[Sejsel]

So, after making sure I rebuilt the correct project, and not running a few months old binary, I am seeing about a 2-2.5 times speedup for my ksplang programs, so this is really nice.

[exyi]

I added benchmarks made from your programs, and yes, it's showing a significant speedup. The following run is inverted, baseline is the new implementation, the current run is with the original funkcia implementation

full_program/aoc24-1-1  time:   [39.805 ms 39.963 ms 40.129 ms]
                        change: [+91.747% +93.078% +94.405%] (p = 0.00 < 0.05)
                        Performance has regressed.
Found 2 outliers among 100 measurements (2.00%)
  2 (2.00%) high mild
full_program/aoc24-1-2  time:   [26.731 ms 26.825 ms 26.921 ms]
                        change: [+71.861% +72.686% +73.534%] (p = 0.00 < 0.05)
                        Performance has regressed.
full_program/aoc24-2-1  time:   [46.007 ms 46.192 ms 46.385 ms]
                        change: [+63.924% +65.121% +66.237%] (p = 0.00 < 0.05)
                        Performance has regressed.
full_program/aoc24-3-2  time:   [104.77 ms 105.14 ms 105.54 ms]
                        change: [+50.228% +50.987% +51.784%] (p = 0.00 < 0.05)
                        Performance has regressed.
full_program/aoc24-7-1  time:   [40.088 ms 40.230 ms 40.379 ms]
                        change: [+59.954% +60.714% +61.503%] (p = 0.00 < 0.05)
                        Performance has regressed.

I also added bit of comments to the implementation, hopefully it makes the algorithm seem less crazy