Proof mode, second draft

[MauroToscano]

Proof mode, second draft

Description

Add proof mode for cairo1 inside the VM.

TODO:

• Solve issue with gas builtin pointer when it's between other built ins
• Add SegmentArena support for dictionaries

[github-actions]

Benchmark Results for unmodified programs 🚀

Command	Mean [s]	Min [s]	Max [s]	Relative
base big_factorial	2.560 ± 0.051	2.526	2.701	1.01 ± 0.02
head big_factorial	2.545 ± 0.006	2.537	2.555	1.00

Command	Mean [s]	Min [s]	Max [s]	Relative
base big_fibonacci	2.155 ± 0.012	2.137	2.169	1.00
head big_fibonacci	2.167 ± 0.017	2.138	2.205	1.01 ± 0.01

Command	Mean [s]	Min [s]	Max [s]	Relative
base blake2s_integration_benchmark	6.003 ± 0.040	5.954	6.094	1.00 ± 0.01
head blake2s_integration_benchmark	5.994 ± 0.039	5.901	6.029	1.00

Command	Mean [s]	Min [s]	Max [s]	Relative
base compare_arrays_200000	2.234 ± 0.015	2.213	2.261	1.00
head compare_arrays_200000	2.237 ± 0.011	2.220	2.252	1.00 ± 0.01

Command	Mean [s]	Min [s]	Max [s]	Relative
base dict_integration_benchmark	1.560 ± 0.007	1.551	1.571	1.00
head dict_integration_benchmark	1.568 ± 0.007	1.555	1.578	1.00 ± 0.01

Command	Mean [s]	Min [s]	Max [s]	Relative
base field_arithmetic_get_square_benchmark	1.053 ± 0.016	1.040	1.096	1.00
head field_arithmetic_get_square_benchmark	1.053 ± 0.019	1.042	1.106	1.00 ± 0.02

Command	Mean [s]	Min [s]	Max [s]	Relative
base integration_builtins	5.906 ± 0.036	5.857	5.973	1.00
head integration_builtins	5.922 ± 0.035	5.872	5.974	1.00 ± 0.01

Command	Mean [s]	Min [s]	Max [s]	Relative
base keccak_integration_benchmark	6.133 ± 0.045	6.055	6.193	1.01 ± 0.02
head keccak_integration_benchmark	6.091 ± 0.116	6.011	6.405	1.00

Command	Mean [s]	Min [s]	Max [s]	Relative
base linear_search	2.272 ± 0.013	2.255	2.301	1.00 ± 0.01
head linear_search	2.269 ± 0.010	2.255	2.285	1.00

Command	Mean [s]	Min [s]	Max [s]	Relative
base math_cmp_and_pow_integration_benchmark	1.559 ± 0.007	1.551	1.572	1.00
head math_cmp_and_pow_integration_benchmark	1.579 ± 0.011	1.564	1.606	1.01 ± 0.01

Command	Mean [s]	Min [s]	Max [s]	Relative
base math_integration_benchmark	1.476 ± 0.017	1.456	1.516	1.00
head math_integration_benchmark	1.488 ± 0.038	1.463	1.595	1.01 ± 0.03

Command	Mean [s]	Min [s]	Max [s]	Relative
base memory_integration_benchmark	1.294 ± 0.013	1.278	1.323	1.00
head memory_integration_benchmark	1.301 ± 0.007	1.290	1.311	1.00 ± 0.01

Command	Mean [s]	Min [s]	Max [s]	Relative
base operations_with_data_structures_benchmarks	1.431 ± 0.011	1.419	1.460	1.00 ± 0.01
head operations_with_data_structures_benchmarks	1.431 ± 0.008	1.420	1.447	1.00

Command	Mean [ms]	Min [ms]	Max [ms]	Relative
base pedersen	579.3 ± 1.5	576.9	580.9	1.00
head pedersen	583.1 ± 4.8	579.6	595.3	1.01 ± 0.01

Command	Mean [s]	Min [s]	Max [s]	Relative
base poseidon_integration_benchmark	1.157 ± 0.006	1.148	1.167	1.00
head poseidon_integration_benchmark	1.166 ± 0.006	1.157	1.176	1.01 ± 0.01

Command	Mean [s]	Min [s]	Max [s]	Relative
base secp_integration_benchmark	1.993 ± 0.006	1.984	2.003	1.00
head secp_integration_benchmark	1.999 ± 0.005	1.992	2.007	1.00 ± 0.00

Command	Mean [s]	Min [s]	Max [s]	Relative
base set_integration_benchmark	1.154 ± 0.009	1.147	1.176	1.00
head set_integration_benchmark	1.164 ± 0.007	1.155	1.180	1.01 ± 0.01

Command	Mean [s]	Min [s]	Max [s]	Relative
base uint256_integration_benchmark	3.883 ± 0.095	3.827	4.147	1.01 ± 0.03
head uint256_integration_benchmark	3.843 ± 0.030	3.810	3.902	1.00

[MauroToscano]

Final version done in #1517