Refactored EC-point point calculations.

[orizi]

Summary

Refactored EC point validation and curve operations by extracting common elliptic curve functionality into the EcPointType struct. Added utility methods for calculating curve points and validating if a point lies on the curve, replacing duplicated curve equation implementations across the codebase.

---

Type of change

Please check one:

• Performance improvement

---

Why is this change needed?

The code had multiple implementations of the same elliptic curve operations scattered across different modules. This created maintenance issues and potential inconsistencies when working with EC points. By centralizing these operations in the EcPointType struct, we ensure consistent behavior and make the code more maintainable.

---

What was the behavior or documentation before?

Previously, the curve equation and validation logic was duplicated in multiple places, with hardcoded constants for the curve parameters appearing in both the runner and simulation code. This made it difficult to ensure consistent behavior across different parts of the codebase.

---

What is the behavior or documentation after?

Now all EC point operations use a centralized implementation in the EcPointType struct, which provides methods for:

• Calculating the left-hand side of the curve equation
• Calculating the right-hand side of the curve equation
• Checking if a point is on the curve

This ensures consistent behavior across the codebase and simplifies maintenance.

---

Additional context

This refactoring improves code organization without changing functionality. The centralized implementation makes it easier to update curve operations if needed in the future.

[reviewable-StarkWare]

This change is 

[orizi]

Warning

This pull request is not mergeable via GitHub because a downstack PR is open. Once all requirements are satisfied, merge this PR as a stack on Graphite.
Learn more

• Refactored EC-point point calculations. #9400 👈 (View in Graphite)
• Fixes the declared returned location of box-deconstruct. #9397
• Fixed cost of local_into_box cost. #9396
• Refactored Box getting libfuncs by CellExpression::add_with_const. #9393
• Merged SmallDiffHelper and build_128bit_diff fns. #9392
• Extended SmallDiffHelper documentation. #9391
• Added u128_bound function removing some minor calculations. #9390
• main

This stack of pull requests is managed by Graphite. Learn more about stacking.

[ilyalesokhin-starkware]

crates/cairo-lang-sierra/src/extensions/modules/ec.rs line 34 at r1 (raw file):

    /// The beta parameter of the curve.
    const BETA: Felt252 = Felt252::from_hex_unchecked(
        "0x6f21413efbe40de150e596d72f7a8c5609ad26c15c915c1f4cdfcb99cee9e89",

Consider mentioning that alpha is 1.

Code quote:

    /// The beta parameter of the curve.
    const BETA: Felt252 = Felt252::from_hex_unchecked(
        "0x6f21413efbe40de150e596d72f7a8c5609ad26c15c915c1f4cdfcb99cee9e89",

[ilyalesokhin-starkware]

@ilyalesokhin-starkware reviewed 4 files and all commit messages, and made 1 comment.
Reviewable status: complete! all files reviewed, all discussions resolved (waiting on @liorgold2 and @TomerStarkware).

[TomerStarkware]

@TomerStarkware reviewed all commit messages and made 1 comment.
Reviewable status: complete! all files reviewed, all discussions resolved (waiting on @liorgold2).