Use Montgomery representation for Felts

[FrancoGiachetta]

Use Montgomery representation for Felts

Closes #NA

Introduces Breaking Changes?

Yes/No.

• Created PR in sequencer
• Created PR in starknet-replay
• Updated the starknet-blocks.yml workflow to use these PRs.

These PRs should be merged after this one right away, in that order.

Checklist

• Linked to Github Issue.
• Unit tests added.
• Integration tests added.
• This change requires new documentation.
  • Documentation has been added/updated.

[github-actions]

Benchmark results Main vs HEAD.

Base

Command	Mean [s]	Min [s]	Max [s]	Relative
base dict_insert.cairo (JIT)	2.664 ± 0.084	2.576	2.835	1.06 ± 0.04
base dict_insert.cairo (AOT)	2.513 ± 0.050	2.465	2.640	1.00

Head

Command	Mean [s]	Min [s]	Max [s]	Relative
head dict_insert.cairo (JIT)	2.731 ± 0.031	2.694	2.801	1.03 ± 0.01
head dict_insert.cairo (AOT)	2.647 ± 0.021	2.624	2.688	1.00

Base

Command	Mean [s]	Min [s]	Max [s]	Relative
base dict_snapshot.cairo (JIT)	2.341 ± 0.047	2.295	2.413	1.05 ± 0.04
base dict_snapshot.cairo (AOT)	2.237 ± 0.061	2.170	2.352	1.00

Head

Command	Mean [s]	Min [s]	Max [s]	Relative
head dict_snapshot.cairo (JIT)	2.430 ± 0.027	2.402	2.487	1.02 ± 0.02
head dict_snapshot.cairo (AOT)	2.371 ± 0.031	2.326	2.432	1.00

Base

Command	Mean [s]	Min [s]	Max [s]	Relative
base factorial_2M.cairo (JIT)	2.702 ± 0.075	2.655	2.905	1.01 ± 0.04
base factorial_2M.cairo (AOT)	2.680 ± 0.061	2.595	2.759	1.00

Head

Command	Mean [s]	Min [s]	Max [s]	Relative
head factorial_2M.cairo (JIT)	2.405 ± 0.023	2.375	2.452	1.03 ± 0.01
head factorial_2M.cairo (AOT)	2.346 ± 0.023	2.308	2.381	1.00

Base

Command	Mean [s]	Min [s]	Max [s]	Relative
base fib_2M.cairo (JIT)	2.215 ± 0.036	2.169	2.278	1.01 ± 0.03
base fib_2M.cairo (AOT)	2.187 ± 0.047	2.131	2.285	1.00

Head

Command	Mean [s]	Min [s]	Max [s]	Relative
head fib_2M.cairo (JIT)	2.354 ± 0.064	2.302	2.519	1.04 ± 0.03
head fib_2M.cairo (AOT)	2.269 ± 0.021	2.241	2.299	1.00

Base

Command	Mean [s]	Min [s]	Max [s]	Relative
base heavy_circuit.cairo (JIT)	14.087 ± 0.128	13.941	14.314	1.02 ± 0.01
base heavy_circuit.cairo (AOT)	13.779 ± 0.080	13.634	13.894	1.00

Head

Command	Mean [s]	Min [s]	Max [s]	Relative
head heavy_circuit.cairo (JIT)	13.451 ± 0.136	13.324	13.758	1.04 ± 0.01
head heavy_circuit.cairo (AOT)	12.957 ± 0.097	12.816	13.116	1.00

Base

Command	Mean [s]	Min [s]	Max [s]	Relative
base linear_search.cairo (JIT)	2.443 ± 0.069	2.371	2.576	1.09 ± 0.03
base linear_search.cairo (AOT)	2.236 ± 0.021	2.204	2.271	1.00

Head

Command	Mean [s]	Min [s]	Max [s]	Relative
head linear_search.cairo (JIT)	2.492 ± 0.031	2.449	2.545	1.08 ± 0.02
head linear_search.cairo (AOT)	2.312 ± 0.023	2.279	2.345	1.00

Base

Command	Mean [s]	Min [s]	Max [s]	Relative
base logistic_map.cairo (JIT)	2.507 ± 0.031	2.463	2.552	1.09 ± 0.02
base logistic_map.cairo (AOT)	2.307 ± 0.032	2.265	2.388	1.00

Head

Command	Mean [s]	Min [s]	Max [s]	Relative
head logistic_map.cairo (JIT)	2.447 ± 0.040	2.383	2.515	1.05 ± 0.03
head logistic_map.cairo (AOT)	2.320 ± 0.042	2.244	2.382	1.00

[github-actions]

Benchmarking results

Benchmark for program dict_insert

Open benchmarks

Command	Mean [s]	Min [s]	Max [s]	Relative
Cairo-vm (Rust, Cairo 1)	11.151 ± 0.038	11.103	11.217	6.04 ± 0.06
cairo-native (embedded AOT)	1.845 ± 0.019	1.820	1.869	1.00
cairo-native (embedded JIT using LLVM's ORC Engine)	1.908 ± 0.016	1.889	1.933	1.03 ± 0.01

Benchmark for program dict_snapshot

Open benchmarks

Command	Mean [ms]	Min [ms]	Max [ms]	Relative
Cairo-vm (Rust, Cairo 1)	544.3 ± 12.7	535.9	579.8	1.00
cairo-native (embedded AOT)	1533.8 ± 12.8	1515.2	1549.1	2.82 ± 0.07
cairo-native (embedded JIT using LLVM's ORC Engine)	1647.2 ± 10.5	1630.6	1663.8	3.03 ± 0.07

Benchmark for program factorial_2M

Open benchmarks

Command	Mean [s]	Min [s]	Max [s]	Relative
Cairo-vm (Rust, Cairo 1)	4.979 ± 0.020	4.963	5.013	3.24 ± 0.03
cairo-native (embedded AOT)	1.539 ± 0.012	1.515	1.560	1.00
cairo-native (embedded JIT using LLVM's ORC Engine)	1.580 ± 0.012	1.566	1.597	1.03 ± 0.01

Benchmark for program factorial_2M_inv

Open benchmarks

Command	Mean [s]	Min [s]	Max [s]	Relative
Cairo-vm (Rust, Cairo 1)	12.994 ± 0.093	12.834	13.156	2.13 ± 0.02
cairo-native (embedded AOT)	6.111 ± 0.015	6.097	6.134	1.00
cairo-native (embedded JIT using LLVM's ORC Engine)	6.176 ± 0.035	6.145	6.271	1.01 ± 0.01

Benchmark for program fib_2M

Open benchmarks

Command	Mean [s]	Min [s]	Max [s]	Relative
Cairo-vm (Rust, Cairo 1)	4.929 ± 0.019	4.901	4.953	3.27 ± 0.02
cairo-native (embedded AOT)	1.506 ± 0.008	1.491	1.513	1.00
cairo-native (embedded JIT using LLVM's ORC Engine)	1.555 ± 0.010	1.540	1.567	1.03 ± 0.01

Benchmark for program heavy_circuit

Open benchmarks

Command	Mean [s]	Min [s]	Max [s]	Relative
Cairo-vm (Rust, Cairo 1)	9.758 ± 0.096	9.637	9.921	1.00
cairo-native (embedded AOT)	11.651 ± 0.029	11.607	11.695	1.19 ± 0.01
cairo-native (embedded JIT using LLVM's ORC Engine)	12.112 ± 0.064	12.009	12.260	1.24 ± 0.01

Benchmark for program linear_search

Open benchmarks

Command	Mean [ms]	Min [ms]	Max [ms]	Relative
Cairo-vm (Rust, Cairo 1)	580.5 ± 4.6	572.4	587.7	1.00
cairo-native (embedded AOT)	1576.4 ± 18.4	1558.0	1619.8	2.72 ± 0.04
cairo-native (embedded JIT using LLVM's ORC Engine)	1710.5 ± 12.3	1692.1	1727.3	2.95 ± 0.03

Benchmark for program logistic_map

Open benchmarks

Command	Mean [ms]	Min [ms]	Max [ms]	Relative
Cairo-vm (Rust, Cairo 1)	501.5 ± 11.9	488.5	524.0	1.00
cairo-native (embedded AOT)	1576.8 ± 22.9	1533.9	1612.5	3.14 ± 0.09
cairo-native (embedded JIT using LLVM's ORC Engine)	1667.3 ± 16.5	1648.5	1697.3	3.32 ± 0.09

[github-actions]

✅ Code is now correctly formatted.