Add ecop builtin

[anatgstarkware]

Note

Medium Risk
Adds a new Cairo builtin (ec_op) into the proving pipeline and updates VM layout handling, which can affect trace generation, constraint evaluation, and proof compatibility. While changes are mostly additive, they touch core prover/claim wiring and builtins relocation/padding logic.

Overview
Adds full prover support for the Cairo ec_op builtin. The adapter now relocates/records an ec_op segment, builtins padding/counting includes it, and the prover wires new ec_op_builtin and partial_ec_mul_generic claims/components through claim generation, interaction-claim aggregation, component lists, and debug tooling.

Updates execution/config plumbing. run_and_adapt now accepts a LayoutName and callers default to LayoutName::all_cairo_stwo (with tests adjusted), the preprocessed-trace PreProcessedTraceVariant type is moved to stwo_cairo_common and carried on PreProcessedTrace, and test data is updated to exercise ec_op usage. Separately removes unused mix_into/is_empty helpers and tweaks PackedPartialEcMulGeneric::deduce_output to return a boxed packed result.

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This change is 

[az-starkware]

@az-starkware reviewed 40 files and all commit messages, and made 2 comments.
Reviewable status: 40 of 96 files reviewed, 2 unresolved discussions (waiting on anatgstarkware and gilbens-starkware).

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stwo_cairo_prover/crates/dev_utils/src/vm_utils.rs line 30 at r2 (raw file):

    program_path: &PathBuf,
    program_type: ProgramType,
    no_ecop: bool,

Suggestion:

layout: LayoutName,

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stwo_cairo_prover/crates/prover/src/witness/builtins.rs line 135 at r2 (raw file):

            id: "pedersen_points_small_0".to_owned(),
        }) {
            panic!("Not supporting ec_op_builtin with canonical_small preprocessed trace.")

Why? What is missing to support it?

[anatgstarkware]

@anatgstarkware made 2 comments.
Reviewable status: 33 of 104 files reviewed, 2 unresolved discussions (waiting on az-starkware and gilbens-starkware).

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stwo_cairo_prover/crates/prover/src/witness/builtins.rs line 135 at r2 (raw file):

Previously, az-starkware wrote…

Why? What is missing to support it?

Fixed as we said f2f

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stwo_cairo_prover/crates/dev_utils/src/vm_utils.rs line 30 at r2 (raw file):

    program_path: &PathBuf,
    program_type: ProgramType,
    no_ecop: bool,

Done.

[cursor]

Cursor Bugbot has reviewed your changes and found 1 potential issue.

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[az-starkware]

@az-starkware reviewed 71 files and all commit messages, made 1 comment, and resolved 2 discussions.
Reviewable status: all files reviewed, 1 unresolved discussion (waiting on anatgstarkware and gilbens-starkware).

[ilyalesokhin-starkware]

stwo_cairo_prover/crates/common/src/preprocessed_columns/preprocessed_trace.rs line 72 at r4 (raw file):

    fn from_columns(
        columns: Vec<Box<dyn PreProcessedColumn>>,
        variant: PreProcessedTraceVariant,

Don't you have two sources of truth here?

Code quote:

        columns: Vec<Box<dyn PreProcessedColumn>>,
        variant: PreProcessedTraceVariant,

[ilyalesokhin-starkware]

stwo_cairo_prover/crates/common/src/preprocessed_columns/preprocessed_trace.rs line 72 at r4 (raw file):

Previously, ilyalesokhin-starkware wrote…

Don't you have two sources of truth here?

can you remove the columns argument.