[perf] Use Vec instead of BTreeMap in tree_from_memory

[Golovanov399]

Metric: tracegen
Before: 10,901.18 ms
After: 10,131.55 ms
Percentage gain: -7.1%

Workflow: https://github.com/axiom-crypto/openvm-reth-benchmark/actions/runs/13160394734

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This resolves INT-3236.

Quote from the ticket.
Our current AddressMap.items() returns something sorted by address (more specifically by (address_space, pointer) lexicographically), therefore no need to push it into a BTreeMap, we can push it into Vec and then modify the recursion a little bit.
We can also save on creating the "all-zero" nodes by building them once and then taking the corresponding node every time we need such node for some height. This should in theory always be strictly better, but this is worse now [...].
End of quote.

I also tried to calculate the capacity once and then reserve the exact capacity needed once instead of Vec::new() and .push() every time, but this was slightly slower or at least the same.

[Golovanov399]

@zlangley I couldn't think of a simple way to avoid collecting items

[zlangley]

Doesn't this mean something bad happened at run-time and the proof will fail? Can't we remove this and just leave the assert below?

[Golovanov399]

This will happen when memory size is not divisible by page size, which, if both of these are powers of two, is equivalent to memory size being less than page size. We can assert that this is not the case and modify the tests correspondingly, in principle

[zlangley]

Note: It's a bit unfortunate that MemoryImage is (address_space, pointer) -> F rather than (address_space, label) -> [F; 8]. I feel like this means we have to do a lot of extra work here and at the end of a segment to convert it into both forms.

[jonathanpwang]

LGTM, added some future ideas

[github-actions]

group	app.proof_time_ms	app.cycles	app.cells_used	leaf.proof_time_ms	leaf.cycles	leaf.cells_used
verify_fibair	(-22 [-1.4%]) 1,522	187,385	9,765,005	-	-	-
fibonacci_program	(+17 [+0.3%]) 4,953	1,500,095	51,485,080	-	-	-
regex_program	14,371	1,914,103	165,455,373	-	-	-
ecrecover_program	(-9 [-0.4%]) 2,489	284,567	15,055,723	-	-	-

Commit: 1aa0c56

Benchmark Workflow

[jonathanpwang]

change items() to use par_iter now!

[jonathanpwang]

actually maybe it's too trivial, let's try separately of this PR