[Cairo 1] Load arguments into VM instead of creating them via instructions

[fmoletta]

Changes
Adds the function load_arguments which loads the input arguments (if any) into the VM after initialization and removes the instructions that create these arguments in create_entry_code. This change has no effect on the execution segment.
Adds test to make sure that the program_hash does not depend on the arguments used to run it.

Motive & Context
This PR solves the issue of the program_hash changing depending on the arguments passed to the vm when running it. This happens due to how cairo 1 handles arguments. Cairo 0 doesn't have arguments when running a program, this was circumvented by Cairo 1 by adding instructions to the original program that declare the arguments as constants and insert them into the execution segment (via tempvars) before calling the main function (they also add the builtin and segment arena pointers). While this allows running cairo 1 programs with arguments, it also makes the program (and therefore the program_hash) vary depending on the arguments used, as the arguments are now part of the instructions.
This PR is the later of 3 approaches to solve this issue, the previous three attempts consisted on:

• Removing the create_entry_code altogether [WIP] Remove create_entry_code #1746 (This run into issues due to the segment arena builtin)

• Replacing all instructions that create values in the execution segment with loading them directly into the VM before the run [Cairo 1] Replace hardcoded arguments with vm initialization #1751 (This worked similarly to this PR, but aside from loading the input arguments, it also loaded the builtin bases & segment arena values and removed the instructions that created them. While this solution worked (aka it allowed proving using Stone Prover), it involves more values being magically created, which can reduce the integrity of the proof (see discussion & possible issues))

Discussion & possible issues
As arguments are now loaded into the memory directly instead of being created by a cairo instruction, this could be seen as a hint being the one that creates those values in memory, which means that we won't be able to prove that it was those specific input values that produced an output based on a program as the prover doesn't currently take these arguments as public inputs.

[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):     27.028 s ±  0.010 s    [User: 26.266 s, System: 0.761 s]
  Range (min … max):   27.020 s … 27.035 s    2 runs
 
Benchmark 2: hyper_threading_pr threads: 1
  Time (mean ± σ):     27.131 s ±  0.096 s    [User: 26.459 s, System: 0.672 s]
  Range (min … max):   27.064 s … 27.199 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):     14.781 s ±  0.046 s    [User: 26.870 s, System: 0.770 s]
  Range (min … max):   14.749 s … 14.814 s    2 runs
 
Benchmark 2: hyper_threading_pr threads: 2
  Time (mean ± σ):     14.736 s ±  0.032 s    [User: 26.851 s, System: 0.756 s]
  Range (min … max):   14.714 s … 14.759 s    2 runs
 
Summary
  'hyper_threading_pr threads: 2' ran
    1.00 ± 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):     10.869 s ±  0.590 s    [User: 39.089 s, System: 0.956 s]
  Range (min … max):   10.452 s … 11.286 s    2 runs
 
Benchmark 2: hyper_threading_pr threads: 4
  Time (mean ± σ):     10.956 s ±  0.573 s    [User: 38.827 s, System: 0.958 s]
  Range (min … max):   10.551 s … 11.362 s    2 runs
 
Summary
  'hyper_threading_main threads: 4' ran
    1.01 ± 0.08 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):     10.605 s ±  0.116 s    [User: 39.054 s, System: 0.988 s]
  Range (min … max):   10.523 s … 10.688 s    2 runs
 
Benchmark 2: hyper_threading_pr threads: 6
  Time (mean ± σ):     10.751 s ±  0.016 s    [User: 38.869 s, System: 0.931 s]
  Range (min … max):   10.740 s … 10.762 s    2 runs
 
Summary
  'hyper_threading_main threads: 6' ran
    1.01 ± 0.01 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):     10.445 s ±  0.025 s    [User: 39.333 s, System: 1.004 s]
  Range (min … max):   10.428 s … 10.463 s    2 runs
 
Benchmark 2: hyper_threading_pr threads: 8
  Time (mean ± σ):     10.435 s ±  0.092 s    [User: 39.381 s, System: 0.970 s]
  Range (min … max):   10.370 s … 10.500 s    2 runs
 
Summary
  'hyper_threading_pr threads: 8' ran
    1.00 ± 0.01 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):     10.814 s ±  0.114 s    [User: 39.631 s, System: 1.083 s]
  Range (min … max):   10.733 s … 10.895 s    2 runs
 
Benchmark 2: hyper_threading_pr threads: 16
  Time (mean ± σ):     10.466 s ±  0.130 s    [User: 39.788 s, System: 0.980 s]
  Range (min … max):   10.374 s … 10.558 s    2 runs
 
Summary
  'hyper_threading_pr threads: 16' ran
    1.03 ± 0.02 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	2.033 ± 0.087	1.984	2.267	1.01 ± 0.05
head big_factorial	2.023 ± 0.038	1.986	2.098	1.00

Command	Mean [s]	Min [s]	Max [s]	Relative
base big_fibonacci	1.970 ± 0.014	1.951	1.994	1.00
head big_fibonacci	1.994 ± 0.030	1.960	2.034	1.01 ± 0.02

Command	Mean [s]	Min [s]	Max [s]	Relative
base blake2s_integration_benchmark	7.503 ± 0.121	7.343	7.672	1.00
head blake2s_integration_benchmark	7.593 ± 0.322	7.364	8.440	1.01 ± 0.05

Command	Mean [s]	Min [s]	Max [s]	Relative
base compare_arrays_200000	2.090 ± 0.021	2.071	2.131	1.00
head compare_arrays_200000	2.117 ± 0.061	2.074	2.274	1.01 ± 0.03

Command	Mean [s]	Min [s]	Max [s]	Relative
base dict_integration_benchmark	1.410 ± 0.009	1.402	1.431	1.00
head dict_integration_benchmark	1.418 ± 0.010	1.403	1.436	1.01 ± 0.01

Command	Mean [s]	Min [s]	Max [s]	Relative
base field_arithmetic_get_square_benchmark	1.286 ± 0.017	1.263	1.308	1.00
head field_arithmetic_get_square_benchmark	1.300 ± 0.070	1.257	1.493	1.01 ± 0.06

Command	Mean [s]	Min [s]	Max [s]	Relative
base integration_builtins	7.572 ± 0.099	7.417	7.698	1.00 ± 0.02
head integration_builtins	7.537 ± 0.130	7.386	7.705	1.00

Command	Mean [s]	Min [s]	Max [s]	Relative
base keccak_integration_benchmark	7.854 ± 0.133	7.649	8.102	1.01 ± 0.02
head keccak_integration_benchmark	7.749 ± 0.098	7.636	7.930	1.00

Command	Mean [s]	Min [s]	Max [s]	Relative
base linear_search	2.087 ± 0.031	2.058	2.136	1.01 ± 0.02
head linear_search	2.058 ± 0.025	2.040	2.103	1.00

Command	Mean [s]	Min [s]	Max [s]	Relative
base math_cmp_and_pow_integration_benchmark	1.698 ± 0.011	1.688	1.719	1.00
head math_cmp_and_pow_integration_benchmark	1.699 ± 0.021	1.679	1.755	1.00 ± 0.01

Command	Mean [s]	Min [s]	Max [s]	Relative
base math_integration_benchmark	1.595 ± 0.014	1.582	1.626	1.00 ± 0.01
head math_integration_benchmark	1.594 ± 0.008	1.583	1.608	1.00

Command	Mean [s]	Min [s]	Max [s]	Relative
base memory_integration_benchmark	1.189 ± 0.012	1.179	1.221	1.00 ± 0.01
head memory_integration_benchmark	1.185 ± 0.011	1.173	1.204	1.00

Command	Mean [s]	Min [s]	Max [s]	Relative
base operations_with_data_structures_benchmarks	1.815 ± 0.015	1.798	1.846	1.00
head operations_with_data_structures_benchmarks	1.823 ± 0.016	1.806	1.852	1.00 ± 0.01

Command	Mean [ms]	Min [ms]	Max [ms]	Relative
base pedersen	515.5 ± 3.2	511.5	520.2	1.00
head pedersen	519.2 ± 15.3	510.0	561.3	1.01 ± 0.03

Command	Mean [ms]	Min [ms]	Max [ms]	Relative
base poseidon_integration_benchmark	966.7 ± 4.6	960.8	973.8	1.00
head poseidon_integration_benchmark	974.7 ± 11.2	962.8	1001.8	1.01 ± 0.01

Command	Mean [s]	Min [s]	Max [s]	Relative
base secp_integration_benchmark	1.859 ± 0.017	1.840	1.883	1.00
head secp_integration_benchmark	1.859 ± 0.020	1.834	1.898	1.00 ± 0.01

Command	Mean [ms]	Min [ms]	Max [ms]	Relative
base set_integration_benchmark	644.7 ± 2.8	641.0	649.0	1.00
head set_integration_benchmark	652.4 ± 19.6	638.5	701.6	1.01 ± 0.03

Command	Mean [s]	Min [s]	Max [s]	Relative
base uint256_integration_benchmark	4.179 ± 0.049	4.096	4.248	1.01 ± 0.02
head uint256_integration_benchmark	4.149 ± 0.057	4.077	4.219	1.00

[codecov]

Codecov Report

Attention: Patch coverage is 92.30769% with 7 lines in your changes are missing coverage. Please review.

Project coverage is 94.79%. Comparing base (aecbb3f) to head (6400d09).

Files	Patch %	Lines
cairo1-run/src/cairo_run.rs	92.30%	7 Missing ⚠️

Additional details and impacted files

@@           Coverage Diff           @@
##             main    #1759   +/-   ##
=======================================
  Coverage   94.79%   94.79%           
=======================================
  Files         101      101           
  Lines       38743    38787   +44     
=======================================
+ Hits        36728    36770   +42     
- Misses       2015     2017    +2     

☔ View full report in Codecov by Sentry.
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[pefontana]

Nice one!

[Okm165]

Really good stuff this enables private inputs to the circuits!

[raphaelDkhn]

@fmoletta

Since program arguments are no longer included in the public inputs for the prover, one way to verify that a program has been executed correctly with specific arguments would to return those arguments in the program's output, right?. This way, we ensure that the arguments become part of the public inputs, similar to serialize_word in CairoZero.

Is it correct?