Implement SECP hints required for k1 and r1 curves

[whichqua]

Implement SECP hints required for k1 and r1 curves

Problem: Secp hints are not defined
Solution: Implement them all

Description

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

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):     25.958 s ±  0.021 s    [User: 25.202 s, System: 0.754 s]
  Range (min … max):   25.943 s … 25.973 s    2 runs
 
Benchmark 2: hyper_threading_pr threads: 1
  Time (mean ± σ):     26.471 s ±  0.003 s    [User: 25.728 s, System: 0.742 s]
  Range (min … max):   26.469 s … 26.473 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):     14.897 s ±  0.249 s    [User: 25.969 s, System: 0.817 s]
  Range (min … max):   14.721 s … 15.074 s    2 runs
 
Benchmark 2: hyper_threading_pr threads: 2
  Time (mean ± σ):     15.056 s ±  0.027 s    [User: 26.314 s, System: 0.750 s]
  Range (min … max):   15.037 s … 15.074 s    2 runs
 
Summary
  'hyper_threading_main threads: 2' ran
    1.01 ± 0.02 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):     10.475 s ±  0.266 s    [User: 37.213 s, System: 0.960 s]
  Range (min … max):   10.287 s … 10.662 s    2 runs
 
Benchmark 2: hyper_threading_pr threads: 4
  Time (mean ± σ):     10.693 s ±  0.434 s    [User: 38.393 s, System: 0.922 s]
  Range (min … max):   10.386 s … 11.000 s    2 runs
 
Summary
  'hyper_threading_main threads: 4' ran
    1.02 ± 0.05 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):     10.209 s ±  0.191 s    [User: 37.686 s, System: 0.993 s]
  Range (min … max):   10.074 s … 10.344 s    2 runs
 
Benchmark 2: hyper_threading_pr threads: 6
  Time (mean ± σ):     10.556 s ±  0.363 s    [User: 38.323 s, System: 0.992 s]
  Range (min … max):   10.300 s … 10.813 s    2 runs
 
Summary
  'hyper_threading_main threads: 6' ran
    1.03 ± 0.04 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):     10.429 s ±  0.282 s    [User: 37.730 s, System: 0.916 s]
  Range (min … max):   10.230 s … 10.629 s    2 runs
 
Benchmark 2: hyper_threading_pr threads: 8
  Time (mean ± σ):     10.478 s ±  0.142 s    [User: 38.246 s, System: 0.997 s]
  Range (min … max):   10.377 s … 10.578 s    2 runs
 
Summary
  'hyper_threading_main threads: 8' ran
    1.00 ± 0.03 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):     10.281 s ±  0.138 s    [User: 37.836 s, System: 1.056 s]
  Range (min … max):   10.183 s … 10.379 s    2 runs
 
Benchmark 2: hyper_threading_pr threads: 16
  Time (mean ± σ):     10.376 s ±  0.249 s    [User: 38.681 s, System: 1.135 s]
  Range (min … max):   10.200 s … 10.552 s    2 runs
 
Summary
  'hyper_threading_main threads: 16' ran
    1.01 ± 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	2.035 ± 0.019	2.008	2.060	1.00
head big_factorial	2.087 ± 0.036	2.069	2.187	1.03 ± 0.02

Command	Mean [s]	Min [s]	Max [s]	Relative
base big_fibonacci	1.983 ± 0.021	1.960	2.016	1.00
head big_fibonacci	2.017 ± 0.005	2.010	2.023	1.02 ± 0.01

Command	Mean [s]	Min [s]	Max [s]	Relative
base blake2s_integration_benchmark	7.489 ± 0.162	7.269	7.654	1.00
head blake2s_integration_benchmark	7.639 ± 0.113	7.490	7.790	1.02 ± 0.03

Command	Mean [s]	Min [s]	Max [s]	Relative
base compare_arrays_200000	2.105 ± 0.031	2.076	2.162	1.00
head compare_arrays_200000	2.164 ± 0.040	2.139	2.257	1.03 ± 0.02

Command	Mean [s]	Min [s]	Max [s]	Relative
base dict_integration_benchmark	1.413 ± 0.021	1.392	1.466	1.00
head dict_integration_benchmark	1.436 ± 0.030	1.418	1.503	1.02 ± 0.03

Command	Mean [s]	Min [s]	Max [s]	Relative
base field_arithmetic_get_square_benchmark	1.194 ± 0.014	1.173	1.215	1.00
head field_arithmetic_get_square_benchmark	1.224 ± 0.020	1.204	1.259	1.02 ± 0.02

Command	Mean [s]	Min [s]	Max [s]	Relative
base integration_builtins	7.574 ± 0.135	7.408	7.708	1.00
head integration_builtins	7.719 ± 0.098	7.578	7.857	1.02 ± 0.02

Command	Mean [s]	Min [s]	Max [s]	Relative
base keccak_integration_benchmark	7.963 ± 0.592	7.555	9.540	1.00
head keccak_integration_benchmark	8.129 ± 0.491	7.761	9.340	1.02 ± 0.10

Command	Mean [s]	Min [s]	Max [s]	Relative
base linear_search	2.110 ± 0.066	2.060	2.293	1.00
head linear_search	2.160 ± 0.070	2.124	2.358	1.02 ± 0.05

Command	Mean [s]	Min [s]	Max [s]	Relative
base math_cmp_and_pow_integration_benchmark	1.475 ± 0.011	1.459	1.492	1.00
head math_cmp_and_pow_integration_benchmark	1.495 ± 0.025	1.474	1.563	1.01 ± 0.02

Command	Mean [s]	Min [s]	Max [s]	Relative
base math_integration_benchmark	1.433 ± 0.022	1.412	1.489	1.00
head math_integration_benchmark	1.452 ± 0.028	1.434	1.530	1.01 ± 0.02

Command	Mean [s]	Min [s]	Max [s]	Relative
base memory_integration_benchmark	1.183 ± 0.024	1.167	1.249	1.00
head memory_integration_benchmark	1.191 ± 0.003	1.184	1.197	1.01 ± 0.02

Command	Mean [s]	Min [s]	Max [s]	Relative
base operations_with_data_structures_benchmarks	1.539 ± 0.013	1.522	1.560	1.00
head operations_with_data_structures_benchmarks	1.578 ± 0.038	1.543	1.636	1.02 ± 0.03

Command	Mean [ms]	Min [ms]	Max [ms]	Relative
base pedersen	525.4 ± 10.2	518.2	552.9	1.00 ± 0.02
head pedersen	523.3 ± 0.9	521.9	524.2	1.00

Command	Mean [ms]	Min [ms]	Max [ms]	Relative
base poseidon_integration_benchmark	755.8 ± 4.5	749.0	762.8	1.00
head poseidon_integration_benchmark	759.4 ± 2.1	757.3	764.1	1.00 ± 0.01

Command	Mean [s]	Min [s]	Max [s]	Relative
base secp_integration_benchmark	1.811 ± 0.038	1.787	1.906	1.01 ± 0.03
head secp_integration_benchmark	1.791 ± 0.036	1.770	1.888	1.00

Command	Mean [ms]	Min [ms]	Max [ms]	Relative
base set_integration_benchmark	635.7 ± 2.4	631.4	639.4	1.00 ± 0.01
head set_integration_benchmark	634.5 ± 7.2	630.3	654.6	1.00

Command	Mean [s]	Min [s]	Max [s]	Relative
base uint256_integration_benchmark	4.139 ± 0.065	4.071	4.249	1.00
head uint256_integration_benchmark	4.235 ± 0.081	4.157	4.429	1.02 ± 0.03