chore: bigfield todo fixes

[suyash67]

Bigfield internal audit related cleanup/fixes.

• Simplified data structs: non_native_multiplication_witnesses and non_native_partial_multiplication_witnesses
• Reduced code duplication with new functions like get_binary_basis_limb_witness_indices
• Resolved/removed some of the TODOs

resolves #14662 #14660
resolves AztecProtocol/barretenberg#999
resolves #14658

[suyash67]

added test case for decompose_into_default_range with odd num of bits.

[suyash67]

Renaming, and removed modulus as its not used.

[Copilot]

Pull Request Overview

This PR cleans up and audits the bigfield and circuit builder code by resolving several TODOs, reducing duplicate logic, and renaming data structures for clarity. Key changes include:

• Renaming non_native_field_witnesses to non_native_multiplication_witnesses (with a corresponding partial witness struct) to simplify non‐native field multiplication.
• Refactoring functions (e.g. pow) with improved fast modular exponentiation and updated gate comments.
• Removing outdated TODOs and replacing them with detailed NOTE comments that better explain the rationale and potential optimizations.

Reviewed Changes

Copilot reviewed 7 out of 7 changed files in this pull request and generated no comments.

Show a summary per file

File	Description
barretenberg/cpp/src/barretenberg/ultra_honk/ultra_honk.test.cpp	Updated non‐native multiplication witness usage and removed modulus parameter.
barretenberg/cpp/src/barretenberg/stdlib_circuit_builders/ultra_circuit_builder.hpp	Renamed witness struct and added a new partial multiplication witness struct, updating function APIs accordingly.
barretenberg/cpp/src/barretenberg/stdlib_circuit_builders/ultra_circuit_builder.cpp	Revised dummy gate comments and simplified auxiliary wire population.
barretenberg/cpp/src/barretenberg/stdlib/primitives/bigfield/bigfield_impl.hpp	Refactored the subtraction, division, and pow functions with optimized arithmetic and clearer NOTE comments.
barretenberg/cpp/src/barretenberg/stdlib/primitives/bigfield/bigfield.test.cpp	Removed stale commented code and improved test assertions.
barretenberg/cpp/src/barretenberg/stdlib/primitives/bigfield/bigfield.hpp	Added additional assertions and helper methods for limb management.
barretenberg/cpp/src/barretenberg/circuit_checker/ultra_circuit_builder.test.cpp	Updated tests to match new witness struct names and range constraint behaviors.

Comments suppressed due to low confidence (3)

barretenberg/cpp/src/barretenberg/ultra_honk/ultra_honk.test.cpp:885

• Renaming the witness struct and removing the modulus parameter requires confirming that evaluate_non_native_field_multiplication correctly infers or retrieves modulus information from the provided limbs. Please verify that the downstream logic remains accurate without the explicit modulus argument.

        a_indices, b_indices, q_indices, r_indices, modulus_limbs,

barretenberg/cpp/src/barretenberg/stdlib_circuit_builders/ultra_circuit_builder.hpp:24

• The new naming of the witness struct to non_native_multiplication_witnesses (and introduction of non_native_partial_multiplication_witnesses) improves clarity. Please ensure that all associated functions and call sites are updated consistently to reflect this change.

template <typename FF> struct non_native_multiplication_witnesses {

barretenberg/cpp/src/barretenberg/stdlib/primitives/bigfield/bigfield_impl.hpp:1013

• The new fast modular exponentiation path for constant bigfield elements uses a loop with bitwise shifts and multiplications. Please ensure that edge cases (such as exponent values 0 and 1) are thoroughly tested and that the shift operations correctly update the exponent during each iteration.

    }