feature: implement and test secp hints

[whichqua]

Implement SECP hints required for k1 and r1 curves

Description

This PR implements secp256(k1|r1) hint processing functions and their unit tests in the Cairo VM:

maybe_write_address_to_ap
pack_x_prime
compute_q_mod_prime
compute_ids_high_low
calculate_value
is_on_curve_2 

Failures due to unknown identifiers and missing members; debugging is in progress.

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.

[github-actions]

**Hyper Thereading Benchmark results**




hyperfine -r 2 -n "hyper_threading_main threads: 1" 'RAYON_NUM_THREADS=1 ./hyper_threading_main' -n "hyper_threading_pr threads: 1" 'RAYON_NUM_THREADS=1 ./hyper_threading_pr'
Benchmark 1: hyper_threading_main threads: 1
  Time (mean ± σ):     25.834 s ±  0.038 s    [User: 25.040 s, System: 0.792 s]
  Range (min … max):   25.807 s … 25.860 s    2 runs
 
Benchmark 2: hyper_threading_pr threads: 1
  Time (mean ± σ):     26.443 s ±  0.070 s    [User: 25.750 s, System: 0.692 s]
  Range (min … max):   26.393 s … 26.493 s    2 runs
 
Summary
  'hyper_threading_main threads: 1' ran
    1.02 ± 0.00 times faster than 'hyper_threading_pr threads: 1'




hyperfine -r 2 -n "hyper_threading_main threads: 2" 'RAYON_NUM_THREADS=2 ./hyper_threading_main' -n "hyper_threading_pr threads: 2" 'RAYON_NUM_THREADS=2 ./hyper_threading_pr'
Benchmark 1: hyper_threading_main threads: 2
  Time (mean ± σ):     14.688 s ±  0.050 s    [User: 25.831 s, System: 0.736 s]
  Range (min … max):   14.653 s … 14.724 s    2 runs
 
Benchmark 2: hyper_threading_pr threads: 2
  Time (mean ± σ):     15.062 s ±  0.024 s    [User: 26.291 s, System: 0.750 s]
  Range (min … max):   15.045 s … 15.079 s    2 runs
 
Summary
  'hyper_threading_main threads: 2' ran
    1.03 ± 0.00 times faster than 'hyper_threading_pr threads: 2'




hyperfine -r 2 -n "hyper_threading_main threads: 4" 'RAYON_NUM_THREADS=4 ./hyper_threading_main' -n "hyper_threading_pr threads: 4" 'RAYON_NUM_THREADS=4 ./hyper_threading_pr'
Benchmark 1: hyper_threading_main threads: 4
  Time (mean ± σ):     10.455 s ±  0.347 s    [User: 37.547 s, System: 0.935 s]
  Range (min … max):   10.210 s … 10.701 s    2 runs
 
Benchmark 2: hyper_threading_pr threads: 4
  Time (mean ± σ):     10.833 s ±  0.022 s    [User: 38.221 s, System: 0.945 s]
  Range (min … max):   10.817 s … 10.848 s    2 runs
 
Summary
  'hyper_threading_main threads: 4' ran
    1.04 ± 0.03 times faster than 'hyper_threading_pr threads: 4'




hyperfine -r 2 -n "hyper_threading_main threads: 6" 'RAYON_NUM_THREADS=6 ./hyper_threading_main' -n "hyper_threading_pr threads: 6" 'RAYON_NUM_THREADS=6 ./hyper_threading_pr'
Benchmark 1: hyper_threading_main threads: 6
  Time (mean ± σ):     10.431 s ±  0.110 s    [User: 36.916 s, System: 0.998 s]
  Range (min … max):   10.353 s … 10.508 s    2 runs
 
Benchmark 2: hyper_threading_pr threads: 6
  Time (mean ± σ):     10.727 s ±  0.263 s    [User: 38.541 s, System: 0.926 s]
  Range (min … max):   10.541 s … 10.913 s    2 runs
 
Summary
  'hyper_threading_main threads: 6' ran
    1.03 ± 0.03 times faster than 'hyper_threading_pr threads: 6'




hyperfine -r 2 -n "hyper_threading_main threads: 8" 'RAYON_NUM_THREADS=8 ./hyper_threading_main' -n "hyper_threading_pr threads: 8" 'RAYON_NUM_THREADS=8 ./hyper_threading_pr'
Benchmark 1: hyper_threading_main threads: 8
  Time (mean ± σ):     10.197 s ±  0.176 s    [User: 37.578 s, System: 0.928 s]
  Range (min … max):   10.072 s … 10.321 s    2 runs
 
Benchmark 2: hyper_threading_pr threads: 8
  Time (mean ± σ):     10.461 s ±  0.081 s    [User: 38.564 s, System: 0.921 s]
  Range (min … max):   10.404 s … 10.519 s    2 runs
 
Summary
  'hyper_threading_main threads: 8' ran
    1.03 ± 0.02 times faster than 'hyper_threading_pr threads: 8'




hyperfine -r 2 -n "hyper_threading_main threads: 16" 'RAYON_NUM_THREADS=16 ./hyper_threading_main' -n "hyper_threading_pr threads: 16" 'RAYON_NUM_THREADS=16 ./hyper_threading_pr'
Benchmark 1: hyper_threading_main threads: 16
  Time (mean ± σ):     10.107 s ±  0.238 s    [User: 37.908 s, System: 0.978 s]
  Range (min … max):    9.939 s … 10.276 s    2 runs
 
Benchmark 2: hyper_threading_pr threads: 16
  Time (mean ± σ):     10.546 s ±  0.210 s    [User: 39.027 s, System: 1.010 s]
  Range (min … max):   10.398 s … 10.695 s    2 runs
 
Summary
  'hyper_threading_main threads: 16' ran
    1.04 ± 0.03 times faster than 'hyper_threading_pr threads: 16'

[github-actions]

Benchmark Results for unmodified programs 🚀

Command	Mean [s]	Min [s]	Max [s]	Relative
base big_factorial	2.058 ± 0.044	2.016	2.167	1.00
head big_factorial	2.131 ± 0.052	2.077	2.250	1.04 ± 0.03

Command	Mean [s]	Min [s]	Max [s]	Relative
base big_fibonacci	2.045 ± 0.052	1.984	2.156	1.01 ± 0.03
head big_fibonacci	2.030 ± 0.013	2.012	2.048	1.00

Command	Mean [s]	Min [s]	Max [s]	Relative
base blake2s_integration_benchmark	7.493 ± 0.182	7.302	7.814	1.00
head blake2s_integration_benchmark	7.699 ± 0.156	7.480	7.862	1.03 ± 0.03

Command	Mean [s]	Min [s]	Max [s]	Relative
base compare_arrays_200000	2.139 ± 0.047	2.089	2.253	1.00
head compare_arrays_200000	2.181 ± 0.043	2.137	2.247	1.02 ± 0.03

Command	Mean [s]	Min [s]	Max [s]	Relative
base dict_integration_benchmark	1.442 ± 0.031	1.419	1.520	1.00
head dict_integration_benchmark	1.458 ± 0.031	1.427	1.521	1.01 ± 0.03

Command	Mean [s]	Min [s]	Max [s]	Relative
base field_arithmetic_get_square_benchmark	1.200 ± 0.028	1.174	1.265	1.00
head field_arithmetic_get_square_benchmark	1.223 ± 0.022	1.203	1.276	1.02 ± 0.03

Command	Mean [s]	Min [s]	Max [s]	Relative
base integration_builtins	7.564 ± 0.164	7.345	7.847	1.00
head integration_builtins	7.840 ± 0.111	7.737	8.071	1.04 ± 0.03

Command	Mean [s]	Min [s]	Max [s]	Relative
base keccak_integration_benchmark	7.899 ± 0.176	7.651	8.235	1.00
head keccak_integration_benchmark	8.100 ± 0.391	7.755	9.143	1.03 ± 0.05

Command	Mean [s]	Min [s]	Max [s]	Relative
base linear_search	2.132 ± 0.040	2.079	2.208	1.00
head linear_search	2.148 ± 0.014	2.128	2.175	1.01 ± 0.02

Command	Mean [s]	Min [s]	Max [s]	Relative
base math_cmp_and_pow_integration_benchmark	1.532 ± 0.032	1.488	1.599	1.00
head math_cmp_and_pow_integration_benchmark	1.553 ± 0.010	1.526	1.560	1.01 ± 0.02

Command	Mean [s]	Min [s]	Max [s]	Relative
base math_integration_benchmark	1.437 ± 0.016	1.422	1.470	1.00
head math_integration_benchmark	1.461 ± 0.021	1.439	1.507	1.02 ± 0.02

Command	Mean [s]	Min [s]	Max [s]	Relative
base memory_integration_benchmark	1.206 ± 0.021	1.171	1.237	1.00
head memory_integration_benchmark	1.241 ± 0.013	1.230	1.265	1.03 ± 0.02

Command	Mean [s]	Min [s]	Max [s]	Relative
base operations_with_data_structures_benchmarks	1.547 ± 0.018	1.530	1.580	1.00
head operations_with_data_structures_benchmarks	1.574 ± 0.017	1.559	1.615	1.02 ± 0.02

Command	Mean [ms]	Min [ms]	Max [ms]	Relative
base pedersen	519.5 ± 2.7	516.6	524.7	1.00
head pedersen	540.2 ± 13.9	530.6	577.7	1.04 ± 0.03

Command	Mean [ms]	Min [ms]	Max [ms]	Relative
base poseidon_integration_benchmark	772.1 ± 7.7	765.2	791.7	1.00
head poseidon_integration_benchmark	774.5 ± 2.7	770.3	778.7	1.00 ± 0.01

Command	Mean [s]	Min [s]	Max [s]	Relative
base secp_integration_benchmark	1.826 ± 0.015	1.806	1.852	1.01 ± 0.01
head secp_integration_benchmark	1.800 ± 0.022	1.771	1.833	1.00

Command	Mean [ms]	Min [ms]	Max [ms]	Relative
base set_integration_benchmark	645.5 ± 5.4	639.6	657.9	1.00
head set_integration_benchmark	660.2 ± 6.5	653.2	671.5	1.02 ± 0.01

Command	Mean [s]	Min [s]	Max [s]	Relative
base uint256_integration_benchmark	4.242 ± 0.163	4.082	4.669	1.00
head uint256_integration_benchmark	4.303 ± 0.056	4.236	4.388	1.01 ± 0.04