feat(hints): add NewHint#49

[MegaRedHand]

Depends on: #1030

Description

This PR adds the missing hint NewHint#49, now known as INV_MOD_P_UINT256.

It also refactors inv_mod_p_uint512, so it uses recently added Uint512 and Uint256 with their pack and split methods.

[MegaRedHand]

Rebased to main after merge of NewHint#47

[github-actions]

Benchmark Results for unmodified programs 🚀

Command	Mean [s]	Min [s]	Max [s]	Relative
base blake2s_integration_benchmark	2.504 ± 0.023	2.477	2.549	1.00
head blake2s_integration_benchmark	2.539 ± 0.025	2.518	2.604	1.01 ± 0.01

Command	Mean [s]	Min [s]	Max [s]	Relative
base compare_arrays_200000	3.108 ± 0.038	3.073	3.196	1.00
head compare_arrays_200000	3.154 ± 0.023	3.129	3.211	1.01 ± 0.01

Command	Mean [s]	Min [s]	Max [s]	Relative
base dict_integration_benchmark	2.427 ± 0.010	2.412	2.446	1.00
head dict_integration_benchmark	2.449 ± 0.018	2.432	2.495	1.01 ± 0.01

Command	Mean [s]	Min [s]	Max [s]	Relative
base factorial_multirun	3.756 ± 0.012	3.736	3.780	1.00
head factorial_multirun	3.821 ± 0.040	3.787	3.915	1.02 ± 0.01

Command	Mean [s]	Min [s]	Max [s]	Relative
base fibonacci_1000_multirun	3.060 ± 0.054	3.009	3.155	1.00
head fibonacci_1000_multirun	3.070 ± 0.015	3.049	3.091	1.00 ± 0.02

Command	Mean [ms]	Min [ms]	Max [ms]	Relative
base field_arithmetic_get_square_benchmark	127.9 ± 1.1	126.4	129.8	1.00
head field_arithmetic_get_square_benchmark	128.1 ± 0.9	127.0	129.6	1.00 ± 0.01

Command	Mean [s]	Min [s]	Max [s]	Relative
base integration_builtins	2.956 ± 0.023	2.935	3.012	1.00
head integration_builtins	3.003 ± 0.008	2.996	3.019	1.02 ± 0.01

Command	Mean [s]	Min [s]	Max [s]	Relative
base keccak_integration_benchmark	2.671 ± 0.025	2.644	2.732	1.00
head keccak_integration_benchmark	2.716 ± 0.028	2.689	2.788	1.02 ± 0.01

Command	Mean [s]	Min [s]	Max [s]	Relative
base linear_search	3.169 ± 0.017	3.150	3.202	1.00
head linear_search	3.247 ± 0.048	3.210	3.378	1.02 ± 0.02

Command	Mean [s]	Min [s]	Max [s]	Relative
base math_cmp_and_pow_integration_benchmark	2.717 ± 0.012	2.696	2.733	1.00
head math_cmp_and_pow_integration_benchmark	2.742 ± 0.016	2.720	2.773	1.01 ± 0.01

Command	Mean [s]	Min [s]	Max [s]	Relative
base math_integration_benchmark	2.482 ± 0.011	2.467	2.504	1.00
head math_integration_benchmark	2.527 ± 0.008	2.514	2.541	1.02 ± 0.01

Command	Mean [s]	Min [s]	Max [s]	Relative
base memory_integration_benchmark	2.149 ± 0.011	2.134	2.170	1.00
head memory_integration_benchmark	2.187 ± 0.011	2.175	2.207	1.02 ± 0.01

Command	Mean [s]	Min [s]	Max [s]	Relative
base operations_with_data_structures_benchmarks	2.221 ± 0.010	2.203	2.237	1.00
head operations_with_data_structures_benchmarks	2.257 ± 0.028	2.233	2.313	1.02 ± 0.01

Command	Mean [ms]	Min [ms]	Max [ms]	Relative
base pedersen	778.2 ± 1.5	775.3	780.6	1.00
head pedersen	790.1 ± 2.4	786.8	795.7	1.02 ± 0.00

Command	Mean [s]	Min [s]	Max [s]	Relative
base poseidon_integration_benchmark	1.516 ± 0.015	1.499	1.545	1.00
head poseidon_integration_benchmark	1.528 ± 0.019	1.510	1.578	1.01 ± 0.02

Command	Mean [s]	Min [s]	Max [s]	Relative
base secp_integration_benchmark	2.372 ± 0.007	2.362	2.386	1.00
head secp_integration_benchmark	2.408 ± 0.009	2.396	2.425	1.01 ± 0.00

Command	Mean [s]	Min [s]	Max [s]	Relative
base set_integration_benchmark	1.694 ± 0.026	1.677	1.766	1.00 ± 0.02
head set_integration_benchmark	1.689 ± 0.006	1.682	1.702	1.00

Command	Mean [s]	Min [s]	Max [s]	Relative
base uint256_integration_benchmark	3.935 ± 0.033	3.900	4.000	1.00
head uint256_integration_benchmark	3.981 ± 0.012	3.957	3.992	1.01 ± 0.01

[codecov]

Codecov Report

Merging #1043 (4a97fa9) into main (4842bf1) will decrease coverage by 0.01%.
The diff coverage is 98.64%.

@@            Coverage Diff             @@
##             main    #1043      +/-   ##
==========================================
- Coverage   98.08%   98.08%   -0.01%     
==========================================
  Files          84       84              
  Lines       33459    33475      +16     
==========================================
+ Hits        32818    32833      +15     
- Misses        641      642       +1     

Impacted Files	Coverage Δ
...rc/hint_processor/builtin_hint_processor/vrf/fq.rs	97.56% <97.61%> (+0.06%)	⬆️
...int_processor/builtin_hint_processor_definition.rs	98.92% <100.00%> (+<0.01%)	⬆️
...or/builtin_hint_processor/vrf/inv_mod_p_uint512.rs	100.00% <100.00%> (ø)

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