chore: remove redundant Felt252<->bytes conversions and simplify

[GarmashAlex]

The signature builtin contained multiple redundant Felt252 byte round-trips (to_bytes_be followed by from_bytes_be) that provided no normalization benefit since Felt252 values in this codebase are already canonical modulo the Cairo prime, and all consumers (including starknet_crypto::verify and the Cairo PIE serializers) accept or serialize felts directly. This change removes those conversions in add_signature, add_validation_rule, get_additional_data, extend_additional_data, and simplifies air_private_input for r and w computation, reducing allocations and improving clarity without altering behavior or formats.

[JulianGCalderon]

Looks good @GarmashAlex! Thanks for the contribution.

[gabrielbosio]

**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):     22.629 s ±  0.042 s    [User: 21.752 s, System: 0.874 s]
  Range (min … max):   22.599 s … 22.658 s    2 runs
 
Benchmark 2: hyper_threading_pr threads: 1
  Time (mean ± σ):     22.732 s ±  0.017 s    [User: 21.876 s, System: 0.853 s]
  Range (min … max):   22.720 s … 22.744 s    2 runs
 
Summary
  hyper_threading_main threads: 1 ran
    1.00 ± 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):     12.121 s ±  0.030 s    [User: 21.729 s, System: 0.872 s]
  Range (min … max):   12.100 s … 12.142 s    2 runs
 
Benchmark 2: hyper_threading_pr threads: 2
  Time (mean ± σ):     12.308 s ±  0.046 s    [User: 22.042 s, System: 0.903 s]
  Range (min … max):   12.276 s … 12.341 s    2 runs
 
Summary
  hyper_threading_main threads: 2 ran
    1.02 ± 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):      9.805 s ±  0.176 s    [User: 34.449 s, System: 1.058 s]
  Range (min … max):    9.681 s …  9.929 s    2 runs
 
Benchmark 2: hyper_threading_pr threads: 4
  Time (mean ± σ):      9.512 s ±  0.111 s    [User: 35.277 s, System: 1.061 s]
  Range (min … max):    9.433 s …  9.590 s    2 runs
 
Summary
  hyper_threading_pr threads: 4 ran
    1.03 ± 0.02 times faster than hyper_threading_main 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):      9.709 s ±  0.021 s    [User: 34.154 s, System: 1.101 s]
  Range (min … max):    9.695 s …  9.724 s    2 runs
 
Benchmark 2: hyper_threading_pr threads: 6
  Time (mean ± σ):      9.747 s ±  0.243 s    [User: 35.057 s, System: 1.064 s]
  Range (min … max):    9.575 s …  9.919 s    2 runs
 
Summary
  hyper_threading_main threads: 6 ran
    1.00 ± 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):      9.442 s ±  0.168 s    [User: 34.847 s, System: 1.109 s]
  Range (min … max):    9.323 s …  9.561 s    2 runs
 
Benchmark 2: hyper_threading_pr threads: 8
  Time (mean ± σ):      9.630 s ±  0.107 s    [User: 35.179 s, System: 1.095 s]
  Range (min … max):    9.554 s …  9.706 s    2 runs
 
Summary
  hyper_threading_main threads: 8 ran
    1.02 ± 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):      9.492 s ±  0.274 s    [User: 35.194 s, System: 1.169 s]
  Range (min … max):    9.299 s …  9.686 s    2 runs
 
Benchmark 2: hyper_threading_pr threads: 16
  Time (mean ± σ):      9.669 s ±  0.230 s    [User: 35.603 s, System: 1.169 s]
  Range (min … max):    9.507 s …  9.832 s    2 runs
 
Summary
  hyper_threading_main threads: 16 ran
    1.02 ± 0.04 times faster than hyper_threading_pr threads: 16

[gabrielbosio]

Benchmark Results for unmodified programs 🚀

Command	Mean [s]	Min [s]	Max [s]	Relative
base big_factorial	1.949 ± 0.013	1.932	1.980	1.00
head big_factorial	1.954 ± 0.008	1.942	1.963	1.00 ± 0.01

Command	Mean [s]	Min [s]	Max [s]	Relative
base big_fibonacci	1.877 ± 0.017	1.864	1.918	1.00
head big_fibonacci	1.890 ± 0.010	1.873	1.908	1.01 ± 0.01

Command	Mean [s]	Min [s]	Max [s]	Relative
base blake2s_integration_benchmark	6.666 ± 0.120	6.528	6.923	1.00
head blake2s_integration_benchmark	6.705 ± 0.071	6.562	6.825	1.01 ± 0.02

Command	Mean [s]	Min [s]	Max [s]	Relative
base compare_arrays_200000	1.989 ± 0.014	1.975	2.020	1.00
head compare_arrays_200000	2.010 ± 0.012	1.993	2.029	1.01 ± 0.01

Command	Mean [s]	Min [s]	Max [s]	Relative
base dict_integration_benchmark	1.327 ± 0.007	1.319	1.339	1.00
head dict_integration_benchmark	1.341 ± 0.007	1.331	1.358	1.01 ± 0.01

Command	Mean [s]	Min [s]	Max [s]	Relative
base field_arithmetic_get_square_benchmark	1.117 ± 0.010	1.106	1.134	1.00
head field_arithmetic_get_square_benchmark	1.140 ± 0.011	1.125	1.157	1.02 ± 0.01

Command	Mean [s]	Min [s]	Max [s]	Relative
base integration_builtins	6.704 ± 0.054	6.659	6.809	1.00
head integration_builtins	6.826 ± 0.056	6.752	6.896	1.02 ± 0.01

Command	Mean [s]	Min [s]	Max [s]	Relative
base keccak_integration_benchmark	6.802 ± 0.087	6.702	6.979	1.00
head keccak_integration_benchmark	6.861 ± 0.069	6.756	6.946	1.01 ± 0.02

Command	Mean [s]	Min [s]	Max [s]	Relative
base linear_search	1.980 ± 0.007	1.974	1.999	1.00
head linear_search	1.995 ± 0.009	1.983	2.008	1.01 ± 0.01

Command	Mean [s]	Min [s]	Max [s]	Relative
base math_cmp_and_pow_integration_benchmark	1.417 ± 0.005	1.410	1.424	1.00
head math_cmp_and_pow_integration_benchmark	1.433 ± 0.006	1.424	1.443	1.01 ± 0.01

Command	Mean [s]	Min [s]	Max [s]	Relative
base math_integration_benchmark	1.372 ± 0.006	1.361	1.381	1.00
head math_integration_benchmark	1.377 ± 0.005	1.365	1.383	1.00 ± 0.01

Command	Mean [s]	Min [s]	Max [s]	Relative
base memory_integration_benchmark	1.123 ± 0.008	1.116	1.142	1.00
head memory_integration_benchmark	1.132 ± 0.014	1.119	1.161	1.01 ± 0.01

Command	Mean [s]	Min [s]	Max [s]	Relative
base operations_with_data_structures_benchmarks	1.446 ± 0.011	1.435	1.470	1.00
head operations_with_data_structures_benchmarks	1.452 ± 0.004	1.445	1.459	1.00 ± 0.01

Command	Mean [ms]	Min [ms]	Max [ms]	Relative
base pedersen	504.3 ± 2.2	502.6	509.9	1.00
head pedersen	505.7 ± 2.1	503.0	509.6	1.00 ± 0.01

Command	Mean [ms]	Min [ms]	Max [ms]	Relative
base poseidon_integration_benchmark	583.7 ± 4.6	578.8	593.6	1.00
head poseidon_integration_benchmark	585.4 ± 2.8	580.1	589.4	1.00 ± 0.01

Command	Mean [s]	Min [s]	Max [s]	Relative
base secp_integration_benchmark	1.709 ± 0.019	1.689	1.749	1.00
head secp_integration_benchmark	1.711 ± 0.005	1.703	1.721	1.00 ± 0.01

Command	Mean [ms]	Min [ms]	Max [ms]	Relative
base set_integration_benchmark	646.5 ± 4.1	644.1	658.0	1.03 ± 0.01
head set_integration_benchmark	629.5 ± 1.5	627.3	631.4	1.00

Command	Mean [s]	Min [s]	Max [s]	Relative
base uint256_integration_benchmark	3.828 ± 0.032	3.794	3.870	1.00
head uint256_integration_benchmark	3.861 ± 0.038	3.825	3.945	1.01 ± 0.01