refactor(ec): store EcState in projective coordinates

[TomerStarkware]

EcState was stored as an affine pair, so every ec_state_add ended in to_affine() — a modular inversion — only for the next add to undo it. Storing the accumulator projectively defers that to a single inversion in ec_state_try_finalize_nz, so the cost of a chain of adds no longer grows with its length.

---

This change is 

[github-actions]

Benchmarking results

Benchmark for program dict_insert

Open benchmarks

Command	Mean [s]	Min [s]	Max [s]	Relative
Cairo-vm (Rust, Cairo 1)	10.586 ± 0.050	10.513	10.685	5.89 ± 0.05
cairo-native (embedded AOT)	1.798 ± 0.014	1.776	1.816	1.00
cairo-native (embedded JIT using LLVM's ORC Engine)	1.813 ± 0.022	1.791	1.856	1.01 ± 0.01

Benchmark for program dict_snapshot

Open benchmarks

Command	Mean [ms]	Min [ms]	Max [ms]	Relative
Cairo-vm (Rust, Cairo 1)	523.9 ± 3.4	519.0	529.6	1.00
cairo-native (embedded AOT)	1650.3 ± 6.9	1641.8	1657.6	3.15 ± 0.02
cairo-native (embedded JIT using LLVM's ORC Engine)	1660.6 ± 12.0	1643.0	1677.3	3.17 ± 0.03

Benchmark for program factorial_2M

Open benchmarks

Command	Mean [s]	Min [s]	Max [s]	Relative
Cairo-vm (Rust, Cairo 1)	4.668 ± 0.040	4.630	4.737	2.72 ± 0.03
cairo-native (embedded AOT)	1.715 ± 0.016	1.697	1.748	1.00
cairo-native (embedded JIT using LLVM's ORC Engine)	1.738 ± 0.023	1.707	1.780	1.01 ± 0.02

Benchmark for program fib_2M

Open benchmarks

Command	Mean [s]	Min [s]	Max [s]	Relative
Cairo-vm (Rust, Cairo 1)	4.677 ± 0.046	4.621	4.778	2.77 ± 0.05
cairo-native (embedded AOT)	1.691 ± 0.026	1.652	1.737	1.00 ± 0.02
cairo-native (embedded JIT using LLVM's ORC Engine)	1.686 ± 0.025	1.643	1.719	1.00

Benchmark for program linear_search

Open benchmarks

Command	Mean [ms]	Min [ms]	Max [ms]	Relative
Cairo-vm (Rust, Cairo 1)	573.3 ± 7.0	563.7	589.4	1.00
cairo-native (embedded AOT)	1688.4 ± 24.0	1651.3	1731.2	2.95 ± 0.06
cairo-native (embedded JIT using LLVM's ORC Engine)	1739.0 ± 15.9	1718.7	1760.0	3.03 ± 0.05

Benchmark for program logistic_map

Open benchmarks

Command	Mean [ms]	Min [ms]	Max [ms]	Relative
Cairo-vm (Rust, Cairo 1)	491.1 ± 6.4	478.7	497.6	1.00
cairo-native (embedded AOT)	1667.0 ± 19.4	1640.0	1708.3	3.39 ± 0.06
cairo-native (embedded JIT using LLVM's ORC Engine)	1677.5 ± 15.2	1657.9	1698.6	3.42 ± 0.05

[github-actions]

Benchmark results Main vs HEAD.

Base

Command	Mean [s]	Min [s]	Max [s]	Relative
base dict_insert.cairo (JIT)	1.475 ± 0.031	1.449	1.539	1.00 ± 0.02
base dict_insert.cairo (AOT)	1.474 ± 0.013	1.456	1.493	1.00

Head

Command	Mean [s]	Min [s]	Max [s]	Relative
head dict_insert.cairo (JIT)	1.746 ± 0.013	1.725	1.772	1.02 ± 0.03
head dict_insert.cairo (AOT)	1.708 ± 0.040	1.665	1.791	1.00

Base

Command	Mean [s]	Min [s]	Max [s]	Relative
base dict_snapshot.cairo (JIT)	1.352 ± 0.018	1.321	1.385	1.00 ± 0.02
base dict_snapshot.cairo (AOT)	1.349 ± 0.018	1.318	1.373	1.00

Head

Command	Mean [s]	Min [s]	Max [s]	Relative
head dict_snapshot.cairo (JIT)	1.529 ± 0.019	1.509	1.575	1.02 ± 0.01
head dict_snapshot.cairo (AOT)	1.505 ± 0.007	1.495	1.518	1.00

Base

Command	Mean [s]	Min [s]	Max [s]	Relative
base factorial_2M.cairo (JIT)	1.409 ± 0.019	1.377	1.439	1.02 ± 0.02
base factorial_2M.cairo (AOT)	1.378 ± 0.018	1.352	1.412	1.00

Head

Command	Mean [s]	Min [s]	Max [s]	Relative
head factorial_2M.cairo (JIT)	1.566 ± 0.008	1.554	1.577	1.01 ± 0.01
head factorial_2M.cairo (AOT)	1.551 ± 0.009	1.541	1.565	1.00

Base

Command	Mean [s]	Min [s]	Max [s]	Relative
base fib_2M.cairo (JIT)	1.386 ± 0.026	1.344	1.433	1.02 ± 0.02
base fib_2M.cairo (AOT)	1.355 ± 0.021	1.318	1.387	1.00

Head

Command	Mean [s]	Min [s]	Max [s]	Relative
head fib_2M.cairo (JIT)	1.514 ± 0.007	1.499	1.524	1.01 ± 0.01
head fib_2M.cairo (AOT)	1.502 ± 0.009	1.490	1.514	1.00

Base

Command	Mean [s]	Min [s]	Max [s]	Relative
base linear_search.cairo (JIT)	1.367 ± 0.017	1.351	1.400	1.01 ± 0.02
base linear_search.cairo (AOT)	1.351 ± 0.013	1.323	1.366	1.00

Head

Command	Mean [s]	Min [s]	Max [s]	Relative
head linear_search.cairo (JIT)	1.578 ± 0.012	1.566	1.600	1.02 ± 0.01
head linear_search.cairo (AOT)	1.551 ± 0.010	1.542	1.575	1.00

Base

Command	Mean [s]	Min [s]	Max [s]	Relative
base logistic_map.cairo (JIT)	1.362 ± 0.014	1.346	1.390	1.02 ± 0.02
base logistic_map.cairo (AOT)	1.335 ± 0.015	1.314	1.362	1.00

Head

Command	Mean [s]	Min [s]	Max [s]	Relative
head logistic_map.cairo (JIT)	1.548 ± 0.010	1.528	1.558	1.02 ± 0.01
head logistic_map.cairo (AOT)	1.524 ± 0.008	1.507	1.532	1.00

[orizi]

@orizi reviewed 19 files and all commit messages, and made 1 comment.
Reviewable status: complete! all files reviewed, all discussions resolved (waiting on TomerStarkware).