feat: add LowLevel.GF16Mul for GF(2^16) field multiplication

[rootulp]

Summary

Expose a thin public wrapper around the existing internal GF(2^16) log/exp table arithmetic in leopard.go, as a method on the existing LowLevel type:

• LowLevel.GF16Mul(a, b uint16) uint16 — multiplies two elements in GF(2^16) using the existing logLUT/expLUT tables. Initializes lazily on first use via the existing sync.Once-guarded initConstants.

No new math or tables are introduced — this is purely a public API surface over already-existing internals.

Motivation

Celestia currently maintains a fork of this repository solely to access GF(2^16) field multiplication for their data availability layer. The diff is small: master...celestiaorg:reedsolomon:master

Upstreaming this allows us to drop the fork and depend on this repo directly.

Test plan

• TestGF16MulZero — anything × 0 = 0
• TestGF16MulOne — multiplicative identity
• TestGF16MulCommutativity — a×b = b×a
• TestGF16MulAssociativity — (a×b)×c = a×(b×c)
• TestGF16MulDistributivity — a×(b⊕c) = a×b ⊕ a×c (GF addition is XOR)
• TestGF16MulConsistentWithInternal — agrees with internal mulLog

🤖 Generated with Claude Code

Summary by CodeRabbit

• New Features

  • Added GF(2^16) multiplication functionality for finite field operations.

• Tests

  • Added comprehensive unit tests validating mathematical properties including zero behavior, multiplicative identity, commutativity, associativity, and distributivity.

[coderabbitai]

No actionable comments were generated in the recent review. 🎉

ℹ️ Recent review info

⚙️ Run configuration

Configuration used: Organization UI

Review profile: CHILL

Plan: Pro

Run ID: af8e96f3-1cea-4c14-a4bd-f5ebd85e878d

📥 Commits

Reviewing files that changed from the base of the PR and between 1840903 and 9eac6ab.

📒 Files selected for processing (2)

• gf16.go
• gf16_test.go

🚧 Files skipped from review as they are similar to previous changes (2)

• gf16_test.go
• gf16.go

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📝 Walkthrough

Walkthrough

Adds a new method GF16Mul to the reedsolomon package implementing GF(2^16) multiplication using precomputed log/exp lookup tables with lazy initialization via initConstants(), plus unit tests validating algebraic properties and edge cases.

Changes

Cohort / File(s)	Summary
Implementation gf16.go	Adds func (l LowLevel) GF16Mul(a, b uint16) uint16 which lazily calls initConstants(), returns 0 if either operand is 0, computes multiplication via logLUT/expLUT with modular reduction, and uses a LowLevel receiver. No other public declarations changed.
Tests gf16_test.go	Adds tests verifying multiplication by zero and one, commutativity, associativity, distributivity (XOR as addition), and consistency with internal mulLog/lookup-table behavior across representative and boundary values.

🚥 Pre-merge checks | ✅ 2 | ❌ 1

❌ Failed checks (1 warning)

Check name	Status	Explanation	Resolution
Docstring Coverage	⚠️ Warning	Docstring coverage is 25.00% which is insufficient. The required threshold is 80.00%.	Write docstrings for the functions missing them to satisfy the coverage threshold.

✅ Passed checks (2 passed)

Check name	Status	Explanation
Description Check	✅ Passed	Check skipped - CodeRabbit’s high-level summary is enabled.
Title check	✅ Passed	The title accurately describes the main change: adding a GF16Mul method to the LowLevel type for GF(2^16) field multiplication, which is exactly what the changeset delivers.

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[coderabbitai]

Actionable comments posted: 1

🤖 Prompt for all review comments with AI agents

Verify each finding against the current code and only fix it if needed.

Inline comments:
In `@gf16.go`:
- Around line 3-7: The doc comment on GF16Init is misleading—update it to state
that GF16Init is optional (it calls initConstants()) and not required because
GF16Mul performs lazy initialization on first use; specifically, change the
sentence "This must be called before using GF16Mul" to indicate the function
precomputes tables for performance but GF16Mul will call initConstants() itself
if needed. Reference: GF16Init, GF16Mul, and initConstants.

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ℹ️ Review info

⚙️ Run configuration

Configuration used: Organization UI

Review profile: CHILL

Plan: Pro

Run ID: 3194888a-155f-4bdd-bba6-a12a1e4b7555

📥 Commits

Reviewing files that changed from the base of the PR and between 182993e and 987764f.

📒 Files selected for processing (2)

• gf16.go
• gf16_test.go

[rootulp]

This seems like a flake unrelated to this PR: https://github.com/klauspost/reedsolomon/actions/runs/22743003914/job/65960582716?pr=327

[rootulp]

CI passed on re-trigger

[rootulp]

Thanks for the review @klauspost! I addressed feedback.

[klauspost]

arm64 crash in #328

I will probably do a release once that is in.

[rootulp]

I see #328 was resolved so will wait for the release and bump to it in celestia-app.

Thanks for your hard work maintaining this repo!

[klauspost]

Didn't want to release on a Friday, since I wouldn't be available for fixes. Released https://github.com/klauspost/reedsolomon/releases/tag/v1.13.3