[Cairo1] Append return values to the output segment when running in proof_mode

[fmoletta]

This involves:

• Forcing the output builtin to be included when running cairo 1 programs in proof_mode (And manually setting it's stop_ptr and segment_size)
• Adding extra instructions in the proof_mode_header (after calling the first program instruction and before initiating the infinite loop) to copy the return values into the output builtin segment

Testing:

• This new behaviour was tested manually by printing out the memory when running the available test programs to ensure that it behaves correctly with one or more return values and all flags enabled.

• There is currently no way to create a test for this behaviour without some code refactors that escape the scope of the PR.

Also in this PR:

• Restored a test that was accidentally removed when solving merge conflicts in a previous PR

[github-actions[bot]]

Benchmark Results for unmodified programs :rocket:

Command	Mean [s]	Min [s]	Max [s]	Relative
base big_factorial	2.285 ± 0.007	2.271	2.295	1.00 ± 0.00
head big_factorial	2.280 ± 0.009	2.269	2.295	1.00

Command	Mean [s]	Min [s]	Max [s]	Relative
base big_fibonacci	2.266 ± 0.009	2.256	2.287	1.00
head big_fibonacci	2.275 ± 0.010	2.264	2.294	1.00 ± 0.01

Command	Mean [s]	Min [s]	Max [s]	Relative
base blake2s_integration_benchmark	8.286 ± 0.044	8.208	8.356	1.00 ± 0.01
head blake2s_integration_benchmark	8.273 ± 0.044	8.235	8.370	1.00

Command	Mean [s]	Min [s]	Max [s]	Relative
base compare_arrays_200000	2.336 ± 0.025	2.310	2.384	1.01 ± 0.01
head compare_arrays_200000	2.318 ± 0.014	2.297	2.343	1.00

Command	Mean [s]	Min [s]	Max [s]	Relative
base dict_integration_benchmark	1.458 ± 0.004	1.451	1.464	1.00
head dict_integration_benchmark	1.460 ± 0.010	1.452	1.486	1.00 ± 0.01

Command	Mean [s]	Min [s]	Max [s]	Relative
base field_arithmetic_get_square_benchmark	1.300 ± 0.017	1.287	1.338	1.00 ± 0.01
head field_arithmetic_get_square_benchmark	1.294 ± 0.007	1.282	1.304	1.00

Command	Mean [s]	Min [s]	Max [s]	Relative
base integration_builtins	8.311 ± 0.038	8.267	8.392	1.00
head integration_builtins	8.344 ± 0.058	8.280	8.447	1.00 ± 0.01

Command	Mean [s]	Min [s]	Max [s]	Relative
base keccak_integration_benchmark	8.596 ± 0.131	8.504	8.952	1.01 ± 0.02
head keccak_integration_benchmark	8.546 ± 0.059	8.490	8.675	1.00

Command	Mean [s]	Min [s]	Max [s]	Relative
base linear_search	2.348 ± 0.014	2.335	2.384	1.00
head linear_search	2.356 ± 0.023	2.328	2.416	1.00 ± 0.01

Command	Mean [s]	Min [s]	Max [s]	Relative
base math_cmp_and_pow_integration_benchmark	1.594 ± 0.013	1.585	1.630	1.01 ± 0.01
head math_cmp_and_pow_integration_benchmark	1.582 ± 0.005	1.575	1.591	1.00

Command	Mean [s]	Min [s]	Max [s]	Relative
base math_integration_benchmark	1.454 ± 0.012	1.446	1.489	1.00 ± 0.01
head math_integration_benchmark	1.452 ± 0.014	1.439	1.490	1.00

Command	Mean [s]	Min [s]	Max [s]	Relative
base memory_integration_benchmark	1.273 ± 0.005	1.268	1.284	1.01 ± 0.01
head memory_integration_benchmark	1.266 ± 0.004	1.262	1.271	1.00

Command	Mean [s]	Min [s]	Max [s]	Relative
base operations_with_data_structures_benchmarks	1.609 ± 0.010	1.597	1.629	1.00
head operations_with_data_structures_benchmarks	1.636 ± 0.019	1.609	1.662	1.02 ± 0.01

Command	Mean [ms]	Min [ms]	Max [ms]	Relative
base pedersen	611.1 ± 10.4	605.6	640.4	1.01 ± 0.02
head pedersen	606.7 ± 2.5	603.0	611.5	1.00

Command	Mean [s]	Min [s]	Max [s]	Relative
base poseidon_integration_benchmark	1.058 ± 0.005	1.054	1.070	1.00
head poseidon_integration_benchmark	1.064 ± 0.005	1.058	1.073	1.01 ± 0.01

Command	Mean [s]	Min [s]	Max [s]	Relative
base secp_integration_benchmark	1.935 ± 0.011	1.925	1.964	1.00
head secp_integration_benchmark	1.941 ± 0.018	1.927	1.989	1.00 ± 0.01

Command	Mean [ms]	Min [ms]	Max [ms]	Relative
base set_integration_benchmark	755.6 ± 5.0	752.0	768.9	1.00 ± 0.01
head set_integration_benchmark	754.4 ± 4.3	750.6	765.8	1.00

Command	Mean [s]	Min [s]	Max [s]	Relative
base uint256_integration_benchmark	4.567 ± 0.032	4.528	4.629	1.00
head uint256_integration_benchmark	4.576 ± 0.036	4.536	4.632	1.00 ± 0.01

[codecov[bot]]

Codecov Report

Attention: 2 lines in your changes are missing coverage. Please review.

Comparison is base (dea2723) 97.13% compared to head (982894d) 97.16%.

Files	Patch %	Lines
cairo1-run/src/main.rs	98.27%	1 Missing :warning:
vm/src/vm/vm_core.rs	87.50%	1 Missing :warning:

Additional details and impacted files

```diff @@ Coverage Diff @@ ## main #1597 +/- ## ========================================== + Coverage 97.13% 97.16% +0.02% ========================================== Files 91 91 Lines 37263 37324 +61 ========================================== + Hits 36196 36264 +68 + Misses 1067 1060 -7 ```

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[juanbono]

We should work on adding the required changes to test this