feat(hints): Implement NewHint#63 & NewHint#65

[fmoletta]

TITLE

Description

Description of the pull request changes and motivation.

Checklist

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

[codecov]

Codecov Report

Merging #1047 (eded3f3) into main (4842bf1) will increase coverage by 0.00%.
The diff coverage is 100.00%.

@@           Coverage Diff           @@
##             main    #1047   +/-   ##
=======================================
  Coverage   98.08%   98.08%           
=======================================
  Files          84       84           
  Lines       33459    33521   +62     
=======================================
+ Hits        32818    32880   +62     
  Misses        641      641           

Impacted Files	Coverage Δ
...int_processor/builtin_hint_processor_definition.rs	98.92% <100.00%> (+<0.01%)	⬆️
...int_processor/builtin_hint_processor/math_utils.rs	97.89% <100.00%> (+0.08%)	⬆️

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[github-actions]

Benchmark Results for unmodified programs 🚀

Command	Mean [s]	Min [s]	Max [s]	Relative
base blake2s_integration_benchmark	3.320 ± 0.085	3.263	3.552	1.01 ± 0.03
head blake2s_integration_benchmark	3.281 ± 0.054	3.231	3.413	1.00

Command	Mean [s]	Min [s]	Max [s]	Relative
base compare_arrays_200000	4.048 ± 0.042	3.977	4.108	1.01 ± 0.02
head compare_arrays_200000	3.996 ± 0.074	3.936	4.177	1.00

Command	Mean [s]	Min [s]	Max [s]	Relative
base dict_integration_benchmark	3.054 ± 0.049	2.994	3.148	1.01 ± 0.02
head dict_integration_benchmark	3.036 ± 0.039	2.989	3.106	1.00

Command	Mean [s]	Min [s]	Max [s]	Relative
base factorial_multirun	4.872 ± 0.062	4.801	5.010	1.01 ± 0.02
head factorial_multirun	4.832 ± 0.099	4.738	5.096	1.00

Command	Mean [s]	Min [s]	Max [s]	Relative
base fibonacci_1000_multirun	3.907 ± 0.029	3.860	3.955	1.01 ± 0.01
head fibonacci_1000_multirun	3.883 ± 0.021	3.848	3.911	1.00

Command	Mean [ms]	Min [ms]	Max [ms]	Relative
base field_arithmetic_get_square_benchmark	153.3 ± 1.4	150.9	155.2	1.01 ± 0.01
head field_arithmetic_get_square_benchmark	152.3 ± 1.4	150.0	154.0	1.00

Command	Mean [s]	Min [s]	Max [s]	Relative
base integration_builtins	3.847 ± 0.023	3.811	3.875	1.02 ± 0.02
head integration_builtins	3.790 ± 0.056	3.712	3.862	1.00

Command	Mean [s]	Min [s]	Max [s]	Relative
base keccak_integration_benchmark	3.581 ± 0.031	3.513	3.637	1.04 ± 0.01
head keccak_integration_benchmark	3.447 ± 0.020	3.422	3.479	1.00

Command	Mean [s]	Min [s]	Max [s]	Relative
base linear_search	4.120 ± 0.070	4.012	4.200	1.00
head linear_search	4.124 ± 0.062	4.057	4.262	1.00 ± 0.02

Command	Mean [s]	Min [s]	Max [s]	Relative
base math_cmp_and_pow_integration_benchmark	3.470 ± 0.041	3.424	3.569	1.02 ± 0.02
head math_cmp_and_pow_integration_benchmark	3.405 ± 0.049	3.332	3.495	1.00

Command	Mean [s]	Min [s]	Max [s]	Relative
base math_integration_benchmark	3.044 ± 0.024	3.014	3.098	1.00
head math_integration_benchmark	3.086 ± 0.026	3.048	3.132	1.01 ± 0.01

Command	Mean [s]	Min [s]	Max [s]	Relative
base memory_integration_benchmark	2.708 ± 0.027	2.648	2.745	1.00
head memory_integration_benchmark	2.723 ± 0.022	2.677	2.751	1.01 ± 0.01

Command	Mean [s]	Min [s]	Max [s]	Relative
base operations_with_data_structures_benchmarks	2.735 ± 0.018	2.710	2.776	1.00
head operations_with_data_structures_benchmarks	2.764 ± 0.027	2.725	2.789	1.01 ± 0.01

Command	Mean [ms]	Min [ms]	Max [ms]	Relative
base pedersen	923.5 ± 11.3	905.1	943.3	1.00 ± 0.01
head pedersen	921.5 ± 7.3	913.6	936.6	1.00

Command	Mean [s]	Min [s]	Max [s]	Relative
base poseidon_integration_benchmark	1.733 ± 0.020	1.712	1.779	1.00
head poseidon_integration_benchmark	1.748 ± 0.012	1.722	1.761	1.01 ± 0.01

Command	Mean [s]	Min [s]	Max [s]	Relative
base secp_integration_benchmark	3.113 ± 0.036	3.040	3.175	1.00
head secp_integration_benchmark	3.154 ± 0.367	3.006	4.197	1.01 ± 0.12

Command	Mean [s]	Min [s]	Max [s]	Relative
base set_integration_benchmark	2.259 ± 0.019	2.225	2.284	1.05 ± 0.06
head set_integration_benchmark	2.144 ± 0.113	2.073	2.413	1.00

Command	Mean [s]	Min [s]	Max [s]	Relative
base uint256_integration_benchmark	4.823 ± 0.059	4.708	4.882	1.00
head uint256_integration_benchmark	4.840 ± 0.098	4.725	5.061	1.00 ± 0.02