Implement air_private_input

[fmoletta]

Adds CairoRunner::get_air_public_input method which outputs a compact AirPrivateInput struct with all builtin's private inputs, which can be converted to an AirPrivateInputSerializable struct that also contains the memory and trace file paths, and matches the file output of the python vm when serialized.
Adds air_private_input flag to cli

[github-actions]

Benchmark Results for unmodified programs 🚀

Command	Mean [s]	Min [s]	Max [s]	Relative
base big_factorial	2.171 ± 0.007	2.161	2.185	1.00
head big_factorial	2.268 ± 0.017	2.247	2.298	1.04 ± 0.01

Command	Mean [s]	Min [s]	Max [s]	Relative
base big_fibonacci	2.133 ± 0.020	2.101	2.161	1.00
head big_fibonacci	2.233 ± 0.023	2.213	2.267	1.05 ± 0.01

Command	Mean [s]	Min [s]	Max [s]	Relative
base blake2s_integration_benchmark	7.818 ± 0.063	7.766	7.934	1.00
head blake2s_integration_benchmark	8.188 ± 0.090	8.096	8.310	1.05 ± 0.01

Command	Mean [s]	Min [s]	Max [s]	Relative
base compare_arrays_200000	2.194 ± 0.014	2.181	2.221	1.00
head compare_arrays_200000	2.279 ± 0.022	2.250	2.315	1.04 ± 0.01

Command	Mean [s]	Min [s]	Max [s]	Relative
base dict_integration_benchmark	1.402 ± 0.011	1.391	1.422	1.00
head dict_integration_benchmark	1.439 ± 0.013	1.429	1.470	1.03 ± 0.01

Command	Mean [s]	Min [s]	Max [s]	Relative
base field_arithmetic_get_square_benchmark	1.243 ± 0.008	1.230	1.255	1.00
head field_arithmetic_get_square_benchmark	1.289 ± 0.010	1.276	1.305	1.04 ± 0.01

Command	Mean [s]	Min [s]	Max [s]	Relative
base integration_builtins	7.901 ± 0.085	7.821	8.112	1.00
head integration_builtins	8.274 ± 0.079	8.174	8.382	1.05 ± 0.02

Command	Mean [s]	Min [s]	Max [s]	Relative
base keccak_integration_benchmark	8.175 ± 0.047	8.111	8.215	1.00
head keccak_integration_benchmark	8.512 ± 0.075	8.415	8.627	1.04 ± 0.01

Command	Mean [s]	Min [s]	Max [s]	Relative
base linear_search	2.231 ± 0.015	2.220	2.269	1.00
head linear_search	2.313 ± 0.026	2.292	2.373	1.04 ± 0.01

Command	Mean [s]	Min [s]	Max [s]	Relative
base math_cmp_and_pow_integration_benchmark	1.520 ± 0.014	1.512	1.560	1.00
head math_cmp_and_pow_integration_benchmark	1.586 ± 0.013	1.572	1.613	1.04 ± 0.01

Command	Mean [s]	Min [s]	Max [s]	Relative
base math_integration_benchmark	1.388 ± 0.007	1.379	1.400	1.00
head math_integration_benchmark	1.447 ± 0.009	1.435	1.464	1.04 ± 0.01

Command	Mean [s]	Min [s]	Max [s]	Relative
base memory_integration_benchmark	1.211 ± 0.002	1.207	1.213	1.00
head memory_integration_benchmark	1.252 ± 0.010	1.239	1.268	1.03 ± 0.01

Command	Mean [s]	Min [s]	Max [s]	Relative
base operations_with_data_structures_benchmarks	1.561 ± 0.006	1.551	1.573	1.00
head operations_with_data_structures_benchmarks	1.629 ± 0.011	1.620	1.652	1.04 ± 0.01

Command	Mean [ms]	Min [ms]	Max [ms]	Relative
base pedersen	596.3 ± 3.0	592.6	600.7	1.00
head pedersen	605.9 ± 2.2	602.9	610.0	1.02 ± 0.01

Command	Mean [s]	Min [s]	Max [s]	Relative
base poseidon_integration_benchmark	1.065 ± 0.007	1.059	1.083	1.00
head poseidon_integration_benchmark	1.075 ± 0.003	1.072	1.082	1.01 ± 0.01

Command	Mean [s]	Min [s]	Max [s]	Relative
base secp_integration_benchmark	1.891 ± 0.004	1.887	1.899	1.00
head secp_integration_benchmark	1.935 ± 0.006	1.928	1.945	1.02 ± 0.00

Command	Mean [ms]	Min [ms]	Max [ms]	Relative
base set_integration_benchmark	762.3 ± 1.2	760.5	764.5	1.00
head set_integration_benchmark	772.1 ± 3.1	767.8	777.4	1.01 ± 0.00

Command	Mean [s]	Min [s]	Max [s]	Relative
base uint256_integration_benchmark	4.381 ± 0.032	4.335	4.432	1.00
head uint256_integration_benchmark	4.523 ± 0.027	4.495	4.571	1.03 ± 0.01

[codecov]

Codecov Report

Attention: 15 lines in your changes are missing coverage. Please review.

Comparison is base (8b9aabe) 97.21% compared to head (b20da7d) 97.21%.
Report is 2 commits behind head on main.

Files	Patch %	Lines
vm/src/vm/runners/builtin_runner/bitwise.rs	96.72%	2 Missing ⚠️
vm/src/vm/runners/builtin_runner/ec_op.rs	95.83%	2 Missing ⚠️
vm/src/vm/runners/builtin_runner/keccak.rs	97.05%	2 Missing ⚠️
vm/src/vm/runners/builtin_runner/poseidon.rs	96.42%	2 Missing ⚠️
vm/src/vm/runners/builtin_runner/range_check.rs	93.75%	2 Missing ⚠️
cairo1-run/src/main.rs	98.24%	1 Missing ⚠️
vm/src/air_private_input.rs	97.82%	1 Missing ⚠️
vm/src/types/relocatable.rs	80.00%	1 Missing ⚠️
vm/src/vm/runners/builtin_runner/hash.rs	98.18%	1 Missing ⚠️
vm/src/vm/runners/builtin_runner/signature.rs	96.29%	1 Missing ⚠️

Additional details and impacted files

@@           Coverage Diff            @@
##             main    #1552    +/-   ##
========================================
  Coverage   97.21%   97.21%            
========================================
  Files          90       91     +1     
  Lines       36452    36990   +538     
========================================
+ Hits        35437    35961   +524     
- Misses       1015     1029    +14     

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