Fix WRITE_DIVMOD_SEGMENT hint

[JulianGCalderon]

Fix WRITE_DIVMOD_SEGMENT hint

We were using SECP_P prime instead of PRIME, as indicated by the hint code.

Additionally, I refactored the hint logic to:

• Return an error variant instead of an assert.
• Improve legibility.

[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):     26.360 s ±  0.038 s    [User: 25.525 s, System: 0.832 s]
  Range (min … max):   26.333 s … 26.386 s    2 runs
 
Benchmark 2: hyper_threading_pr threads: 1
  Time (mean ± σ):     26.192 s ±  0.028 s    [User: 25.392 s, System: 0.796 s]
  Range (min … max):   26.172 s … 26.212 s    2 runs
 
Summary
  hyper_threading_pr threads: 1 ran
    1.01 ± 0.00 times faster than hyper_threading_main 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):     14.634 s ±  0.066 s    [User: 25.640 s, System: 0.813 s]
  Range (min … max):   14.587 s … 14.681 s    2 runs
 
Benchmark 2: hyper_threading_pr threads: 2
  Time (mean ± σ):     14.536 s ±  0.014 s    [User: 25.437 s, System: 0.808 s]
  Range (min … max):   14.527 s … 14.546 s    2 runs
 
Summary
  hyper_threading_pr threads: 2 ran
    1.01 ± 0.00 times faster than hyper_threading_main 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):     10.446 s ±  0.126 s    [User: 37.607 s, System: 1.001 s]
  Range (min … max):   10.356 s … 10.535 s    2 runs
 
Benchmark 2: hyper_threading_pr threads: 4
  Time (mean ± σ):     10.556 s ±  0.226 s    [User: 37.510 s, System: 0.970 s]
  Range (min … max):   10.396 s … 10.716 s    2 runs
 
Summary
  hyper_threading_main threads: 4 ran
    1.01 ± 0.02 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):     10.243 s ±  0.271 s    [User: 38.076 s, System: 1.014 s]
  Range (min … max):   10.051 s … 10.435 s    2 runs
 
Benchmark 2: hyper_threading_pr threads: 6
  Time (mean ± σ):     10.555 s ±  0.016 s    [User: 38.136 s, System: 1.018 s]
  Range (min … max):   10.544 s … 10.566 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):     10.415 s ±  0.219 s    [User: 37.709 s, System: 1.007 s]
  Range (min … max):   10.260 s … 10.569 s    2 runs
 
Benchmark 2: hyper_threading_pr threads: 8
  Time (mean ± σ):     10.213 s ±  0.009 s    [User: 38.374 s, System: 1.011 s]
  Range (min … max):   10.207 s … 10.220 s    2 runs
 
Summary
  hyper_threading_pr threads: 8 ran
    1.02 ± 0.02 times faster than hyper_threading_main 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):     10.562 s ±  0.058 s    [User: 38.223 s, System: 1.100 s]
  Range (min … max):   10.521 s … 10.603 s    2 runs
 
Benchmark 2: hyper_threading_pr threads: 16
  Time (mean ± σ):     10.164 s ±  0.055 s    [User: 38.420 s, System: 1.124 s]
  Range (min … max):   10.125 s … 10.202 s    2 runs
 
Summary
  hyper_threading_pr threads: 16 ran
    1.04 ± 0.01 times faster than hyper_threading_main threads: 16

[github-actions]

Benchmark Results for unmodified programs 🚀

Command	Mean [s]	Min [s]	Max [s]	Relative
base big_factorial	2.136 ± 0.009	2.124	2.151	1.00 ± 0.01
head big_factorial	2.128 ± 0.013	2.109	2.150	1.00

Command	Mean [s]	Min [s]	Max [s]	Relative
base big_fibonacci	2.055 ± 0.008	2.041	2.065	1.00
head big_fibonacci	2.060 ± 0.021	2.044	2.110	1.00 ± 0.01

Command	Mean [s]	Min [s]	Max [s]	Relative
base blake2s_integration_benchmark	7.589 ± 0.034	7.546	7.639	1.00 ± 0.01
head blake2s_integration_benchmark	7.580 ± 0.063	7.541	7.752	1.00

Command	Mean [s]	Min [s]	Max [s]	Relative
base compare_arrays_200000	2.217 ± 0.015	2.203	2.254	1.00
head compare_arrays_200000	2.220 ± 0.022	2.203	2.256	1.00 ± 0.01

Command	Mean [s]	Min [s]	Max [s]	Relative
base dict_integration_benchmark	1.455 ± 0.014	1.441	1.488	1.00 ± 0.02
head dict_integration_benchmark	1.453 ± 0.019	1.437	1.499	1.00

Command	Mean [s]	Min [s]	Max [s]	Relative
base field_arithmetic_get_square_benchmark	1.231 ± 0.003	1.224	1.234	1.00
head field_arithmetic_get_square_benchmark	1.235 ± 0.011	1.226	1.262	1.00 ± 0.01

Command	Mean [s]	Min [s]	Max [s]	Relative
base integration_builtins	7.665 ± 0.035	7.589	7.707	1.00
head integration_builtins	7.679 ± 0.102	7.616	7.958	1.00 ± 0.01

Command	Mean [s]	Min [s]	Max [s]	Relative
base keccak_integration_benchmark	7.919 ± 0.096	7.865	8.188	1.01 ± 0.01
head keccak_integration_benchmark	7.871 ± 0.023	7.835	7.906	1.00

Command	Mean [s]	Min [s]	Max [s]	Relative
base linear_search	2.208 ± 0.057	2.177	2.368	1.01 ± 0.03
head linear_search	2.180 ± 0.007	2.168	2.193	1.00

Command	Mean [s]	Min [s]	Max [s]	Relative
base math_cmp_and_pow_integration_benchmark	1.548 ± 0.021	1.532	1.606	1.00 ± 0.02
head math_cmp_and_pow_integration_benchmark	1.543 ± 0.019	1.524	1.580	1.00

Command	Mean [s]	Min [s]	Max [s]	Relative
base math_integration_benchmark	1.486 ± 0.012	1.475	1.518	1.00 ± 0.01
head math_integration_benchmark	1.484 ± 0.004	1.481	1.492	1.00

Command	Mean [s]	Min [s]	Max [s]	Relative
base memory_integration_benchmark	1.235 ± 0.018	1.226	1.287	1.00
head memory_integration_benchmark	1.239 ± 0.028	1.220	1.318	1.00 ± 0.03

Command	Mean [s]	Min [s]	Max [s]	Relative
base operations_with_data_structures_benchmarks	1.595 ± 0.006	1.588	1.608	1.00 ± 0.00
head operations_with_data_structures_benchmarks	1.594 ± 0.004	1.589	1.601	1.00

Command	Mean [ms]	Min [ms]	Max [ms]	Relative
base pedersen	537.3 ± 1.5	535.4	539.2	1.00 ± 0.00
head pedersen	535.5 ± 1.6	532.8	538.0	1.00

Command	Mean [ms]	Min [ms]	Max [ms]	Relative
base poseidon_integration_benchmark	651.5 ± 3.2	645.8	654.6	1.00 ± 0.01
head poseidon_integration_benchmark	650.4 ± 3.4	644.8	654.6	1.00

Command	Mean [s]	Min [s]	Max [s]	Relative
base secp_integration_benchmark	1.885 ± 0.016	1.870	1.921	1.01 ± 0.01
head secp_integration_benchmark	1.872 ± 0.007	1.865	1.889	1.00

Command	Mean [ms]	Min [ms]	Max [ms]	Relative
base set_integration_benchmark	633.2 ± 5.8	629.2	649.3	1.00 ± 0.01
head set_integration_benchmark	630.6 ± 1.6	628.1	632.6	1.00

Command	Mean [s]	Min [s]	Max [s]	Relative
base uint256_integration_benchmark	4.244 ± 0.016	4.221	4.270	1.00 ± 0.01
head uint256_integration_benchmark	4.244 ± 0.016	4.216	4.267	1.00

[codecov]

Codecov Report

All modified and coverable lines are covered by tests ✅

Project coverage is 96.58%. Comparing base (f2b63ff) to head (937fe62).
Report is 1 commits behind head on main.

Additional details and impacted files

@@           Coverage Diff           @@
##             main    #2078   +/-   ##
=======================================
  Coverage   96.58%   96.58%           
=======================================
  Files         102      102           
  Lines       42924    42924           
=======================================
  Hits        41456    41456           
  Misses       1468     1468           

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