I'm not able to comment on what this code is doing, but as for the theory:
The halting problem is only unsolvable in the general case. You cannot prove that any arbitrary piece of code will stop, but you can prove that specific types of code will stop and reject anything that you're unable to prove. The trivial case is "no jumps"—if your code executes strictly linearly and is itself finite then you know it will terminate. More advanced cases can also be proven, like a loop over a very specific bound, as long as you can place constraints on how the code can be structured.
As an example, take a look at Dafny, which places a lot of restrictions on loops [0], only allowing the subset that it can effectively analyze.
Adding on (and it's not terribly relevant to eBPF), it's also worth noting that there are trivial programs you can prove DON'T halt.
A trivial example[1]:
int main() {
while (true) {}
int x = foo();
return x;
}
This program trivially runs forever[2], and indeed many static code analyzers will point out that everything after the `while (true) {}` line is unreachable.
I feel like the halting problem is incredibly widely misunderstood to be similar to be about "ANY program" when it really talks about "ALL programs".
[1]: In C++, this is undefined behavior technically, but C and most other programming languages define the behavior of this (or equivalent) function.
The halting problem is only unsolvable in the general case. You cannot prove that any arbitrary piece of code will stop, but you can prove that specific types of code will stop and reject anything that you're unable to prove. The trivial case is "no jumps"—if your code executes strictly linearly and is itself finite then you know it will terminate. More advanced cases can also be proven, like a loop over a very specific bound, as long as you can place constraints on how the code can be structured.
As an example, take a look at Dafny, which places a lot of restrictions on loops [0], only allowing the subset that it can effectively analyze.
[0] https://ece.uwaterloo.ca/~agurfink/stqam/rise4fun-Dafny/#h25