Make air public inputs deserializable

[fmoletta]

Derives Deserialize trait for PublicInput
Note: dynamic layout params are currently ignored when deserializing, see #1649

[github-actions]

Benchmark Results for unmodified programs 🚀

Command	Mean [s]	Min [s]	Max [s]	Relative
base big_factorial	2.318 ± 0.083	2.278	2.551	1.00
head big_factorial	2.347 ± 0.095	2.279	2.611	1.01 ± 0.05

Command	Mean [s]	Min [s]	Max [s]	Relative
base big_fibonacci	2.288 ± 0.027	2.245	2.324	1.01 ± 0.02
head big_fibonacci	2.262 ± 0.030	2.231	2.306	1.00

Command	Mean [s]	Min [s]	Max [s]	Relative
base blake2s_integration_benchmark	8.590 ± 0.102	8.471	8.809	1.00
head blake2s_integration_benchmark	8.682 ± 0.188	8.461	8.911	1.01 ± 0.02

Command	Mean [s]	Min [s]	Max [s]	Relative
base compare_arrays_200000	2.401 ± 0.027	2.362	2.443	1.00
head compare_arrays_200000	2.410 ± 0.030	2.374	2.478	1.00 ± 0.02

Command	Mean [s]	Min [s]	Max [s]	Relative
base dict_integration_benchmark	1.492 ± 0.010	1.476	1.508	1.00 ± 0.01
head dict_integration_benchmark	1.488 ± 0.011	1.473	1.505	1.00

Command	Mean [s]	Min [s]	Max [s]	Relative
base field_arithmetic_get_square_benchmark	1.344 ± 0.014	1.325	1.365	1.00 ± 0.02
head field_arithmetic_get_square_benchmark	1.343 ± 0.017	1.326	1.372	1.00

Command	Mean [s]	Min [s]	Max [s]	Relative
base integration_builtins	8.770 ± 0.258	8.524	9.437	1.00 ± 0.04
head integration_builtins	8.739 ± 0.172	8.469	8.949	1.00

Command	Mean [s]	Min [s]	Max [s]	Relative
base keccak_integration_benchmark	8.917 ± 0.147	8.726	9.102	1.00
head keccak_integration_benchmark	8.969 ± 0.165	8.701	9.148	1.01 ± 0.02

Command	Mean [s]	Min [s]	Max [s]	Relative
base linear_search	2.388 ± 0.021	2.367	2.422	1.00
head linear_search	2.419 ± 0.037	2.376	2.500	1.01 ± 0.02

Command	Mean [s]	Min [s]	Max [s]	Relative
base math_cmp_and_pow_integration_benchmark	1.634 ± 0.029	1.605	1.699	1.01 ± 0.02
head math_cmp_and_pow_integration_benchmark	1.614 ± 0.007	1.606	1.626	1.00

Command	Mean [s]	Min [s]	Max [s]	Relative
base math_integration_benchmark	1.466 ± 0.008	1.454	1.477	1.00 ± 0.01
head math_integration_benchmark	1.465 ± 0.012	1.444	1.486	1.00

Command	Mean [s]	Min [s]	Max [s]	Relative
base memory_integration_benchmark	1.305 ± 0.009	1.294	1.315	1.00
head memory_integration_benchmark	1.309 ± 0.006	1.302	1.322	1.00 ± 0.01

Command	Mean [s]	Min [s]	Max [s]	Relative
base operations_with_data_structures_benchmarks	1.652 ± 0.020	1.636	1.703	1.01 ± 0.01
head operations_with_data_structures_benchmarks	1.643 ± 0.011	1.625	1.662	1.00

Command	Mean [ms]	Min [ms]	Max [ms]	Relative
base pedersen	601.3 ± 6.3	597.0	616.4	1.00
head pedersen	605.6 ± 16.3	596.3	647.9	1.01 ± 0.03

Command	Mean [ms]	Min [ms]	Max [ms]	Relative
base poseidon_integration_benchmark	995.0 ± 5.4	987.7	1003.5	1.01 ± 0.01
head poseidon_integration_benchmark	989.0 ± 5.9	980.8	999.9	1.00

Command	Mean [s]	Min [s]	Max [s]	Relative
base secp_integration_benchmark	1.911 ± 0.017	1.891	1.948	1.00
head secp_integration_benchmark	1.925 ± 0.027	1.898	1.993	1.01 ± 0.02

Command	Mean [ms]	Min [ms]	Max [ms]	Relative
base set_integration_benchmark	723.3 ± 3.8	719.0	731.1	1.01 ± 0.01
head set_integration_benchmark	718.0 ± 4.4	710.9	726.1	1.00

Command	Mean [s]	Min [s]	Max [s]	Relative
base uint256_integration_benchmark	4.771 ± 0.060	4.693	4.852	1.00
head uint256_integration_benchmark	4.798 ± 0.068	4.694	4.867	1.01 ± 0.02

[codecov]

Codecov Report

Attention: Patch coverage is 65.38462% with 9 lines in your changes are missing coverage. Please review.

Project coverage is 97.66%. Comparing base (59a97c7) to head (8f89325).

Files	Patch %	Lines
vm/src/air_public_input.rs	65.38%	9 Missing ⚠️

Additional details and impacted files

@@            Coverage Diff             @@
##             main    #1648      +/-   ##
==========================================
- Coverage   97.68%   97.66%   -0.02%     
==========================================
  Files          91       91              
  Lines       37689    37712      +23     
==========================================
+ Hits        36817    36833      +16     
- Misses        872      879       +7     

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