Fix BoundedInt Add libfunc

[DiegoCivi]

Fix BoundedInt Add libfunc

The previous implementation of the add libfunc had some cases in which it failed to return the correct result. We decided to change the algorithm to one that is simpler to understand and that fixes the errors.

We have C = A + B, where all of them are BoundedInt. We represent the a BoundedInt as:

• X = Xo + Xd, where
  • X is a BoundedInt.
  • Xo is the lower bound of the BoundedInt range.
  • Xd is the offset.

So we want to get Cd and we have Co + Cd = Ao + Ad + Bo + Bd -> Cd = Ao + Ad + Bo + Bd - Co. When having BoundedInt additions we need to implement the AddHelper like the following:

impl AddHelper of AddHelper<BoundedInt<1, 30>, BoundedInt<0, 10>> {
    type Result = BoundedInt<1, 40>;
}

fn run_addition() -> BoundedInt<1, 40> {
    let a: BoundedInt<1, 30> = 10.try_into().unwrap();
    let b: BoundedInt<0, 10> = 5.try_into().unwrap();
    return add(a, b);
}

In this case we have:

• Ao = 1
• Ad = 9
• Bo = 0
• Bd = 5
• Co = 1

And as we can see Co = Ao + Bo. If this is not satisfied, then the Cairo code won´t compile. Then, by having Cd = Ao + Ad + Bo + Bd - Co and Co = Ao + Bo we can simplify the addition to Cd = Ad + Bd.

Closes #1448

Introduces Breaking Changes?

No.

Checklist

• Linked to Github Issue.
• Unit tests added.
• Integration tests added.
• This change requires new documentation.
  • Documentation has been added/updated.

[codecov-commenter]

Codecov Report

❌ Patch coverage is 80.00000% with 6 lines in your changes missing coverage. Please review.
✅ Project coverage is 81.50%. Comparing base (2241ffb) to head (32fa505).

Files with missing lines	Patch %	Lines
src/libfuncs/bounded_int.rs	80.00%	6 Missing ⚠️

Additional details and impacted files

@@           Coverage Diff           @@
##             main    #1463   +/-   ##
=======================================
  Coverage   81.50%   81.50%           
=======================================
  Files         105      105           
  Lines       25868    25858   -10     
=======================================
- Hits        21084    21076    -8     
+ Misses       4784     4782    -2     

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[github-actions]

Benchmark results Main vs HEAD.

Base

Command	Mean [s]	Min [s]	Max [s]	Relative
base dict_insert.cairo (JIT)	2.548 ± 0.011	2.528	2.566	1.04 ± 0.01
base dict_insert.cairo (AOT)	2.453 ± 0.021	2.429	2.492	1.00

Head

Command	Mean [s]	Min [s]	Max [s]	Relative
head dict_insert.cairo (JIT)	2.571 ± 0.032	2.532	2.626	1.03 ± 0.01
head dict_insert.cairo (AOT)	2.489 ± 0.015	2.464	2.509	1.00

Base

Command	Mean [s]	Min [s]	Max [s]	Relative
base dict_snapshot.cairo (JIT)	2.257 ± 0.018	2.228	2.290	1.06 ± 0.01
base dict_snapshot.cairo (AOT)	2.139 ± 0.017	2.105	2.175	1.00

Head

Command	Mean [s]	Min [s]	Max [s]	Relative
head dict_snapshot.cairo (JIT)	2.278 ± 0.014	2.259	2.305	1.04 ± 0.01
head dict_snapshot.cairo (AOT)	2.184 ± 0.018	2.162	2.223	1.00

Base

Command	Mean [s]	Min [s]	Max [s]	Relative
base factorial_2M.cairo (JIT)	2.619 ± 0.011	2.603	2.637	1.02 ± 0.01
base factorial_2M.cairo (AOT)	2.574 ± 0.010	2.559	2.591	1.00

Head

Command	Mean [s]	Min [s]	Max [s]	Relative
head factorial_2M.cairo (JIT)	2.625 ± 0.016	2.606	2.662	1.01 ± 0.01
head factorial_2M.cairo (AOT)	2.592 ± 0.016	2.561	2.618	1.00

Base

Command	Mean [s]	Min [s]	Max [s]	Relative
base fib_2M.cairo (JIT)	2.151 ± 0.017	2.124	2.188	1.02 ± 0.01
base fib_2M.cairo (AOT)	2.103 ± 0.014	2.084	2.126	1.00

Head

Command	Mean [s]	Min [s]	Max [s]	Relative
head fib_2M.cairo (JIT)	2.181 ± 0.026	2.142	2.217	1.02 ± 0.02
head fib_2M.cairo (AOT)	2.134 ± 0.025	2.099	2.186	1.00

Base

Command	Mean [s]	Min [s]	Max [s]	Relative
base heavy_circuit.cairo (JIT)	14.884 ± 0.040	14.812	14.941	1.03 ± 0.00
base heavy_circuit.cairo (AOT)	14.477 ± 0.040	14.408	14.544	1.00

Head

Command	Mean [s]	Min [s]	Max [s]	Relative
head heavy_circuit.cairo (JIT)	14.024 ± 0.065	13.936	14.127	1.03 ± 0.01
head heavy_circuit.cairo (AOT)	13.624 ± 0.086	13.518	13.790	1.00

Base

Command	Mean [s]	Min [s]	Max [s]	Relative
base linear_search.cairo (JIT)	2.327 ± 0.014	2.308	2.347	1.06 ± 0.01
base linear_search.cairo (AOT)	2.197 ± 0.022	2.163	2.222	1.00

Head

Command	Mean [s]	Min [s]	Max [s]	Relative
head linear_search.cairo (JIT)	2.350 ± 0.013	2.328	2.369	1.05 ± 0.02
head linear_search.cairo (AOT)	2.234 ± 0.035	2.195	2.296	1.00

Base

Command	Mean [s]	Min [s]	Max [s]	Relative
base logistic_map.cairo (JIT)	2.425 ± 0.015	2.397	2.446	1.07 ± 0.01
base logistic_map.cairo (AOT)	2.270 ± 0.014	2.248	2.292	1.00

Head

Command	Mean [s]	Min [s]	Max [s]	Relative
head logistic_map.cairo (JIT)	2.473 ± 0.015	2.451	2.506	1.08 ± 0.01
head logistic_map.cairo (AOT)	2.288 ± 0.017	2.267	2.319	1.00

[github-actions]

Benchmarking results

Benchmark for program dict_insert

Open benchmarks

Command	Mean [s]	Min [s]	Max [s]	Relative
Cairo-vm (Rust, Cairo 1)	10.948 ± 0.060	10.877	11.088	4.55 ± 0.04
cairo-native (embedded AOT)	2.408 ± 0.018	2.372	2.432	1.00
cairo-native (embedded JIT using LLVM's ORC Engine)	2.496 ± 0.023	2.464	2.528	1.04 ± 0.01

Benchmark for program dict_snapshot

Open benchmarks

Command	Mean [ms]	Min [ms]	Max [ms]	Relative
Cairo-vm (Rust, Cairo 1)	519.6 ± 6.8	508.2	527.1	1.00
cairo-native (embedded AOT)	2106.6 ± 16.8	2079.8	2136.8	4.05 ± 0.06
cairo-native (embedded JIT using LLVM's ORC Engine)	2211.6 ± 20.3	2193.2	2257.7	4.26 ± 0.07

Benchmark for program factorial_2M

Open benchmarks

Command	Mean [s]	Min [s]	Max [s]	Relative
Cairo-vm (Rust, Cairo 1)	4.752 ± 0.036	4.724	4.848	1.87 ± 0.02
cairo-native (embedded AOT)	2.538 ± 0.015	2.511	2.557	1.00
cairo-native (embedded JIT using LLVM's ORC Engine)	2.591 ± 0.021	2.563	2.624	1.02 ± 0.01

Benchmark for program fib_2M

Open benchmarks

Command	Mean [s]	Min [s]	Max [s]	Relative
Cairo-vm (Rust, Cairo 1)	4.739 ± 0.087	4.682	4.957	2.29 ± 0.05
cairo-native (embedded AOT)	2.067 ± 0.019	2.034	2.099	1.00
cairo-native (embedded JIT using LLVM's ORC Engine)	2.116 ± 0.010	2.103	2.135	1.02 ± 0.01

Benchmark for program heavy_circuit

Open benchmarks

Command	Mean [s]	Min [s]	Max [s]	Relative
Cairo-vm (Rust, Cairo 1)	9.526 ± 0.056	9.459	9.641	1.00
cairo-native (embedded AOT)	14.467 ± 0.046	14.378	14.523	1.52 ± 0.01
cairo-native (embedded JIT using LLVM's ORC Engine)	14.876 ± 0.066	14.751	14.963	1.56 ± 0.01

Benchmark for program linear_search

Open benchmarks

Command	Mean [ms]	Min [ms]	Max [ms]	Relative
Cairo-vm (Rust, Cairo 1)	563.0 ± 5.4	552.9	572.5	1.00
cairo-native (embedded AOT)	2149.7 ± 14.1	2128.4	2169.0	3.82 ± 0.04
cairo-native (embedded JIT using LLVM's ORC Engine)	2294.4 ± 18.0	2267.6	2332.4	4.08 ± 0.05

Benchmark for program logistic_map

Open benchmarks

Command	Mean [ms]	Min [ms]	Max [ms]	Relative
Cairo-vm (Rust, Cairo 1)	375.1 ± 5.8	369.0	390.1	1.00
cairo-native (embedded AOT)	2228.9 ± 13.5	2209.2	2248.9	5.94 ± 0.10
cairo-native (embedded JIT using LLVM's ORC Engine)	2411.8 ± 16.4	2389.0	2446.3	6.43 ± 0.11

[JulianGCalderon]

LGTM!