hakorune/docs/development/analysis/LOOPFORM_PHI_SOLUTION_SUMMARY.md

LoopForm PHI Solution - Executive Summary

Date: 2025-11-17 Task: Solve ValueId(14)/ValueId(17) circular dependency in multi-carrier loop PHI construction Approach: LoopForm Meta-Box design based on academic SSA literature and Box Theory philosophy

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Problem Statement

Multi-carrier loops (e.g., fibonacci with variables a, b, i) combined with pinned receivers (me parameter) produce invalid MIR:

bb3 (preheader):
   %13 = copy %10   # me
   %15 = copy %0    # limit parameter
   br bb6

bb6 (header):
   %18 = phi [%15, bb3], ...  # ✅ OK - %15 exists in bb3
   %17 = phi [%14, bb3], ...  # ❌ ERROR - %14 doesn't exist in bb3!
   %14 = phi [%13, bb3], ...  # %14 defined HERE

Root Cause: Interleaved ValueId allocation during prepare_loop_variables_with() creates forward references that violate SSA definition-before-use.

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Solution: LoopForm Meta-Box

Core Insight

Treat the entire loop structure as a single "Meta-Box" with explicit separation of:

• Carriers: Variables modified in loop body (i, a, b)
• Pinned: Loop-invariant variables (me, limit parameters)

Key Innovation

Three-Pass Construction:

// Pass 1: Allocate ALL ValueIds upfront
builder.prepare_structure(ops, current_vars)?;
// Result: pinned[0].copy=%100, pinned[0].phi=%101, carrier[0].copy=%102, ...

// Pass 2: Emit preheader block
builder.emit_preheader(ops)?;
// Result: %100 = copy %0; %102 = copy %2; ...

// Pass 3: Emit header PHIs (incomplete)
builder.emit_header_phis(ops)?;
// Result: %101 = phi [%100, bb0]; %103 = phi [%102, bb0]; ...

// Pass 4: Seal PHIs after loop body
// (merge preheader + continue blocks + latch into header PHIs)
builder.seal_phis(ops, latch_id, &continue_snapshots)?;
// Result: %101 = phi [%100, bb0], [%200, bb_cont], [%101, latch];
//         %103 = phi [%102, bb0], [%201, bb_cont], [%120, latch]

Critical Property: All ValueIds allocated in Pass 1, before any MIR emission → no circular dependencies possible.

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Academic Foundation

Braun et al. (2013): Simple and Efficient SSA Construction

Quote: "The φ-function itself becomes the placeholder for the loop variable, preventing forward references."

Application: Our prepare_structure() allocates all φ-IDs upfront, making them valid placeholders before any use.

LLVM Canonical Loop Form

Structure:

preheader → header (PHI nodes) → body → latch → header
                                      ↘ exit

Our Implementation: Matches LLVM canonical form exactly, with explicit preheader copy materialization.

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Implementation

Files Created

1. src/mir/phi_core/loopform_builder.rs (360 lines):

   • LoopFormBuilder struct
   • CarrierVariable and PinnedVariable types
   • LoopFormOps trait (abstraction over MIR builder)
   • Unit tests demonstrating correctness

2. docs/development/analysis/loopform-phi-circular-dependency-solution.md (600+ lines):

   • Comprehensive analysis
   • Academic literature review
   • Alternative approaches considered
   • Detailed implementation plan

Integration Points

Status: 当初は NYASH_LOOPFORM_PHI_V2=1 で opt-in する Feature Flag 案だったが、
現在は LoopFormBuilder を用いた PHI 生成が 常に既定実装 になっている。

過去の段階的移行案（参考・設計メモとして残す）:

// In mir/loop_builder.rs （設計当初の案。現在は v2 が常時有効）
if std::env::var("NYASH_LOOPFORM_PHI_V2").is_ok() {
    // Use new LoopFormBuilder
    let mut loopform = LoopFormBuilder::new(preheader_id, header_id);
    loopform.prepare_structure(ops, current_vars)?;
    loopform.emit_preheader(ops)?;
    loopform.emit_header_phis(ops)?;
    // ... lower loop body ...
    loopform.seal_phis(ops, latch_id)?;
} else {
    // Use existing prepare_loop_variables_with()
    let incomplete_phis = prepare_loop_variables_with(ops, ...)?;
    // ... existing code ...
}

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Advantages

1. Correctness

• Eliminates circular dependencies by design
• Guarantees SSA definition-before-use through explicit passes
• Aligns with academic algorithms (Braun et al., LLVM)

2. Maintainability

• Explicit separation of carriers vs. pinned variables
• Self-documenting code: CarrierVariable vs. PinnedVariable types
• Unit testable: Mock LoopFormOps implementation in tests

3. Performance

• No runtime overhead: All allocation happens once in Pass 1
• Deterministic ordering: Predictable ValueId allocation
• Future optimization: Can skip PHIs for true loop-invariants

4. Box Theory Alignment

• LoopForm as Meta-Box: Treats loop structure itself as a Box
• Preserves simplicity: ~150 lines of core logic (vs. 650 lines in traditional SSA)
• Gradual enhancement: Can extend with nested loops, break/continue without refactoring

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Testing Strategy

Phase 1–3: 現在の運用メモ

• 実装が LoopForm v2 に一本化されたため、NYASH_LOOPFORM_PHI_V2 による A/B 比較フェーズは既に完了済み。
• 以降の性能比較や回帰テストでは、単に ./target/release/nyash を直接叩けばよい（フラグ不要）。

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Migration Timeline

Week 1: Prototype Implementation (DONE ✅)

• Create loopform_builder.rs
• Implement LoopFormBuilder struct
• Add unit tests
• Write comprehensive documentation

Week 2: Integration & Testing

• Add feature flag to mir/loop_builder.rs
• Implement LoopFormOps for existing MIR builder
• Run smoke tests with new implementation
• Fix any integration issues

Week 3: Selfhost Compiler Integration

• Extend selfhost JSON bridge to use LoopForm approach
• Test multi-carrier loops in selfhost path
• Validate Phase 25.1b goals achieved

Week 4: Full Migration

• Enable by default (NYASH_LOOPFORM_PHI_V2=1 becomes default)
• Deprecate old prepare_loop_variables_with() path
• Remove feature flag after confirmation

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Risk Assessment

Low Risk

• No changes to MIR semantics: Same PHI nodes generated, just in correct order
• Feature-flagged rollback: Can disable if issues found
• Extensive testing: Academic algorithms are well-proven

Medium Risk

• Selfhost compiler compatibility: JSON-based approach may need adapter
• Nested loop interaction: Need to test with complex loop patterns

Mitigation

• Gradual rollout: Feature flag allows A/B testing
• Comprehensive smoke tests: Cover all loop patterns before migration
• Academic validation: Algorithm matches proven SSA construction methods

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Success Criteria

Must Have (Week 2)

• fib_multi_carrier.hako produces correct output (8)
• All existing loop smoke tests pass with new implementation
• No performance regression (< 5% slowdown acceptable)

Should Have (Week 3)

• Selfhost compiler uses LoopForm for multi-carrier loops
• Nested loop support validated
• Break/continue with exit PHIs working

Nice to Have (Week 4)

• Loop-invariant optimization (skip PHIs for non-modified vars)
• Extended to support switch statements in loops
• Academic paper draft: "LoopForm Meta-Box: SSA Construction via Box Theory"

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References

1. Academic Papers:

   • Cytron et al. (1991): "Efficiently Computing SSA Form"
   • Braun et al. (2013): "Simple and Efficient SSA Construction"
   • LLVM: Loop Terminology and Canonical Forms

2. Project Documentation:

   • docs/private/research/papers-archive/paper-d-ssa-construction/box-theory-solution.md
   • docs/development/architecture/loops/loopform_ssot.md
   • docs/guides/loopform.md

3. Implementation Files:

   • src/mir/phi_core/loopform_builder.rs (new)
   • src/mir/phi_core/loop_phi.rs (existing)
   • src/mir/loop_builder.rs (to be updated)

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Conclusion

The LoopForm Meta-Box approach provides a theoretically sound, practically simple, and philosophically aligned solution to the PHI circular dependency problem.

By treating loop structure as a first-class "Box" and separating carriers from pinned variables, we eliminate the root cause while preserving the elegance of Box Theory's SSA construction revolution (650 → 100 lines).

Next Action: Integrate LoopFormBuilder into mir/loop_builder.rs with feature flag and validate with fibonacci test.

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Document Status: COMPLETE ✅ Implementation Status: PROTOTYPE READY ✅ Testing Status: UNIT TESTS PASS ✅ Integration Status: PENDING (Week 2)