# Hybrid Bitmap+Magazine Approach: Objective Analysis

**Date**: 2025-10-26
**Proposal**: ChatGPT Pro's "Bitmap = Control Plane, Free-list = Data Plane" hybrid
**Goal**: Achieve both speed (mimalloc-like) and research features (bitmap visibility)
**Status**: Technical feasibility analysis

---

## Executive Summary

### The Proposal

**Core Idea**: "Bitmap on top of Micro-Freelist"
- **Data Plane (hot path)**: Page-level mini-magazine (8-16 items, LIFO free-list)
- **Control Plane (cold path)**: Bitmap as "truth", batch refill/spill
- **Research Features**: Read from bitmap (complete visibility maintained)

### Objective Assessment

**Verdict**: ✅ **Technically sound and promising, but requires careful integration**

| Aspect | Rating | Comment |
|--------|--------|---------|
| **Technical soundness** | ✅ Excellent | Well-established pattern (mimalloc uses similar) |
| **Performance potential** | ✅ Good | 83ns → 45-55ns realistic (35-45% improvement) |
| **Research value** | ✅ Excellent | Bitmap visibility fully preserved |
| **Implementation complexity** | ⚠️ Moderate | 6-8 hours, careful integration needed |
| **Risk** | ⚠️ Moderate | TLS Magazine integration unclear, bitmap lag concerns |

**Recommendation**: **Adopt with modifications** (see Section 8)

---

## 1. Technical Architecture

### 1.1 Current hakmem Tiny Pool Structure

```
┌─────────────────────────────────┐
│ TLS Magazine [2048 items]       │  ← Fast path (magazine hit)
│   items: void* [2048]            │
│   top: int                       │
└────────────┬────────────────────┘
             ↓ (magazine empty)
┌─────────────────────────────────┐
│ TLS Active Slab A/B             │  ← Medium path (bitmap scan)
│   bitmap[16]: uint64_t          │
│   free_count: uint16_t          │
└────────────┬────────────────────┘
             ↓ (slab full)
┌─────────────────────────────────┐
│ Global Pool (mutex-protected)   │  ← Slow path (lock contention)
│   free_slabs[8]: TinySlab*      │
│   full_slabs[8]: TinySlab*      │
└─────────────────────────────────┘

Problem: Bitmap scan on every slab allocation (5-6ns overhead)
```

### 1.2 Proposed Hybrid Structure

```
┌─────────────────────────────────┐
│ Page Mini-Magazine [8-16 items] │  ← Fast path (O(1) LIFO)
│   mag_head: Block*              │     Cost: 1-2ns
│   mag_count: uint8_t            │
└────────────┬────────────────────┘
             ↓ (mini-mag empty)
┌─────────────────────────────────┐
│ Batch Refill from Bitmap        │  ← Medium path (batch of 8)
│   bm_top: uint64_t (summary)    │     Cost: 5-8ns (amortized 1ns/item)
│   bm_word[16]: uint64_t         │
│   refill_batch: 8 items         │
└────────────┬────────────────────┘
             ↓ (bitmap empty)
┌─────────────────────────────────┐
│ New Page or Drain Pending       │  ← Slow path
└─────────────────────────────────┘

Benefit: Fast path is free-list speed, bitmap cost is amortized
```

### 1.3 Key Innovation: Two-Tier Bitmap

**Standard Bitmap** (current hakmem):
```c
uint64_t bitmap[16];  // 1024 bits
// Problem: Must scan 16 words to find first free
for (int i = 0; i < 16; i++) {
    if (bitmap[i] == 0) continue;  // Empty word scan overhead
    // ...
}
// Cost: 2-3ns per word in worst case = 30-50ns total
```

**Two-Tier Bitmap** (proposed):
```c
uint64_t bm_top;       // Summary: 1 bit per word (16 bits used)
uint64_t bm_word[16];  // Data: 64 bits per word

// Fast path: Zero empty scan
if (bm_top == 0) return 0;  // Instant check (1 cycle)

int w = __builtin_ctzll(bm_top);  // First non-empty word (1 cycle)
uint64_t m = bm_word[w];           // Load word (3 cycles)
// Cost: 1.5ns total (vs 30-50ns worst case)
```

**Impact**: Empty scan overhead eliminated ✅

---

## 2. Performance Analysis

### 2.1 Expected Fast Path (Best Case)

```c
static inline void* tiny_alloc_fast(ThreadHeap* th, int class_idx) {
    Page* p = th->active[class_idx];   // 2 ns (L1 TLS hit)
    Block* b = p->mag_head;             // 2 ns (L1 page hit)
    if (likely(b)) {                    // 0.5 ns (predicted taken)
        p->mag_head = b->next;          // 1 ns (L1 write)
        p->mag_count--;                 // 0.5 ns (inc)
        return b;                       // 0.5 ns
    }
    return tiny_alloc_refill(th, p, class_idx);  // Slow path
}
// Total: 6.5 ns (pure CPU, L1 hits)
```

**But reality includes**:
- Size classification: +1 ns (with LUT)
- TLS base load: +1 ns
- Occasional branch mispredict: +5 ns (1 in 20)
- Occasional L2 miss: +10 ns (1 in 50)

**Realistic fast path average**: **12-15 ns** (vs current 83 ns)

### 2.2 Medium Path: Refill from Bitmap

```c
static inline int refill_from_bitmap(Page* p, int want) {
    uint64_t top = p->bm_top;           // 2 ns (L1 hit)
    if (top == 0) return 0;             // 0.5 ns

    int w = __builtin_ctzll(top);       // 1 ns (tzcnt instruction)
    uint64_t m = p->bm_word[w];         // 2 ns (L1 hit)

    int got = 0;
    while (m && got < want) {           // 8 iterations (want=8)
        int bit = __builtin_ctzll(m);   // 1 ns
        m &= (m - 1);                   // 1 ns (clear bit)
        void* blk = index_to_block(...);// 2 ns
        push_to_mag(blk);               // 1 ns
        got++;
    }
    // Total loop: 8 * 5 ns = 40 ns

    p->bm_word[w] = m;                  // 1 ns
    if (!m) p->bm_top &= ~(1ull << w);  // 1 ns
    p->mag_count += got;                // 1 ns
    return got;
}
// Total: 2 + 0.5 + 1 + 2 + 40 + 1 + 1 + 1 = 48.5 ns for 8 items
// Amortized: 6 ns per item
```

**Impact**: Bitmap cost amortized to **6 ns/item** (vs current 5-6 ns/item, but batched)

### 2.3 Overall Expected Performance

**Allocation breakdown** (with 90% mini-mag hit rate):
```
90% fast path:   12 ns * 0.9 = 10.8 ns
10% refill path: 48 ns * 0.1 =  4.8 ns  (includes fast path + refill)
Total average:                  15.6 ns
```

**But this assumes**:
- Mini-magazine always has items (90% hit rate)
- Bitmap refill is infrequent (10%)
- No statistics overhead
- No TLS magazine layer

**More realistic** (accounting for all overheads):
```
Size classification (LUT):       1 ns
TLS Magazine check:              3 ns (if kept)
  OR
Page mini-magazine:              12 ns (if TLS Magazine removed)
Statistics (batched):            2 ns (sampled)
Occasional refill:               5 ns (amortized)
Total:                           20-23 ns (if optimized)
```

**Current baseline**: 83 ns
**Expected with hybrid**: **35-45 ns** (40-55% improvement)

### 2.4 Why Not 12-15 ns?

**Missing overhead in best-case analysis**:
1. **TLS Magazine integration**: Current hakmem has TLS Magazine layer
   - If kept: +10 ns (magazine check overhead)
   - If removed: Simpler but loses current fast path
2. **Statistics**: Even batched, adds 2-3 ns
3. **Refill frequency**: If mini-mag is only 8-16 items, refill happens often
4. **Cache misses**: Real-world workloads have 5-10% L2 misses

**Realistic target**: **35-45 ns** (still 2x faster than current 83 ns!)

---

## 3. Integration with Existing hakmem Structure

### 3.1 Critical Question: What happens to TLS Magazine?

**Current TLS Magazine**:
```c
typedef struct TinyTLSMag {
    TinyItem items[2048];  // 16 KB per class
    int top;
} TinyTLSMag;
static __thread TinyTLSMag g_tls_mags[TINY_NUM_CLASSES];
```

**Options**:

#### Option A: Keep Both (Dual-Layer Cache)
```
TLS Magazine [2048 items]
  ↓ (empty)
Page Mini-Magazine [8-16 items]
  ↓ (empty)
Bitmap Refill
```

**Pros**: Preserves current fast path
**Cons**:
- Double caching overhead (complexity)
- TLS Magazine dominates, mini-magazine rarely used
- **Not recommended** ❌

#### Option B: Remove TLS Magazine (Single-Layer)
```
Page Mini-Magazine [16-32 items]  ← Increase size
  ↓ (empty)
Bitmap Refill [batch of 16]
```

**Pros**: Simpler, clearer hot path
**Cons**:
- Loses current TLS Magazine fast path (1.5 ns/op)
- Requires testing to verify performance
- **Moderate risk** ⚠️

#### Option C: Hybrid (TLS Mini-Magazine)
```
TLS Mini-Magazine [64-128 items per class]
  ↓ (empty)
Refill from Multiple Pages' Bitmaps
  ↓ (all bitmaps empty)
New Page
```

**Pros**: Best of both (TLS speed + bitmap control)
**Cons**:
- More complex refill logic
- **Recommended** ✅

### 3.2 Recommended Structure

```c
typedef struct TinyTLSCache {
    // Fast path: Small TLS magazine
    Block* mag_head;       // LIFO stack (not array)
    uint16_t mag_count;    // Current count
    uint16_t mag_max;      // 64-128 (tunable)

    // Medium path: Active page with bitmap
    Page* active;

    // Cold path: Partial pages list
    Page* partial_head;
} TinyTLSCache;

static __thread TinyTLSCache g_tls_cache[TINY_NUM_CLASSES];
```

**Allocation**:
1. Pop from `mag_head` (1-2 ns) ← Fast path
2. If empty, `refill_from_bitmap(active, 16)` (48 ns, 16 items) → +3 ns amortized
3. If active bitmap empty, swap to partial page
4. If no partial, allocate new page

**Expected**: **12-15 ns average** (90%+ mag hit rate)

---

## 4. Bitmap as "Control Plane": Research Features

### 4.1 Bitmap Consistency Model

**Problem**: Mini-magazine has items, but bitmap still marks them as "free"
```
Bitmap state:  [1 1 1 1 1 1 1 1]  (all free)
Mini-mag:      [b1, b2, b3]      (3 blocks cached)
Truth:         Only 5 are truly free, not 8
```

**Solution 1**: Lazy Update (Eventual Consistency)
```c
// On refill: Mark blocks as allocated in bitmap
void refill_from_bitmap(Page* p, int want) {
    // ... extract blocks ...
    for each block:
        clear_bit(p->bm_word, idx);  // Mark allocated immediately
    // Mini-mag now holds allocated blocks (consistent)
}

// On spill: Mark blocks as free in bitmap
void spill_to_bitmap(Page* p, int count) {
    for each block in mini-mag:
        set_bit(p->bm_word, idx);    // Mark free
}
```

**Consistency**: ✅ Bitmap is always truth, mini-mag is just cache

**Solution 2**: Shadow State
```c
// Bitmap tracks "ever allocated" state
// Mini-mag tracks "currently cached" state
// Research features read: bitmap + mini-mag count

uint16_t get_true_free_count(Page* p) {
    return p->bitmap_free_count - p->mag_count;
}
```

**Consistency**: ⚠️ More complex, but allows instant queries

**Recommendation**: **Solution 1** (simpler, consistent)

### 4.2 Research Features Still Work

**Call-site profiling**:
```c
// On allocation, record call-site
void* alloc_with_profiling(void* site) {
    void* ptr = tiny_alloc_fast(...);

    // Diagnostic: Update bitmap-based tracking
    if (diagnostic_enabled) {
        int idx = block_index(page, ptr);
        page->owner[idx] = current_thread();
        page->alloc_site[idx] = site;
    }
    return ptr;
}
```

**ELO learning**:
```c
// On free, update ELO based on lifetime
void free_with_elo(void* ptr) {
    int idx = block_index(page, ptr);
    void* site = page->alloc_site[idx];
    uint64_t lifetime = rdtsc() - page->alloc_time[idx];

    update_elo(site, lifetime);  // Bitmap enables this

    tiny_free_fast(ptr);  // Then free normally
}
```

**Memory diagnostics**:
```c
// Snapshot: Flush mini-mag to bitmap, then read
void snapshot_memory_state() {
    flush_all_mini_magazines();  // Spill to bitmaps

    for_each_page(page) {
        print_bitmap_state(page);  // Full visibility
    }
}
```

**Conclusion**: ✅ **All research features preserved** (with flush/spill)

---

## 5. Implementation Complexity

### 5.1 Required Changes

**New structures** (~50 lines):
```c
typedef struct Block {
    struct Block* next;  // Intrusive LIFO
} Block;

typedef struct Page {
    // Mini-magazine
    Block* mag_head;
    uint16_t mag_count;
    uint16_t mag_max;

    // Two-tier bitmap
    uint64_t bm_top;
    uint64_t bm_word[16];

    // Existing (keep)
    uint8_t* base;
    uint16_t block_size;
    // ...
} Page;
```

**New functions** (~200 lines):
```c
void* tiny_alloc_fast(ThreadHeap* th, int class_idx);
void tiny_free_fast(Page* p, void* ptr);
int refill_from_bitmap(Page* p, int want);
void spill_to_bitmap(Page* p);
void init_two_tier_bitmap(Page* p);
```

**Modified functions** (~300 lines):
```c
// Existing bitmap allocation → refill logic
hak_tiny_alloc() → integrate with tiny_alloc_fast()
hak_tiny_free() → integrate with tiny_free_fast()
// Statistics collection → batched/sampled
```

**Total code changes**: ~500-600 lines (moderate)

### 5.2 Testing Requirements

**Unit tests**:
- Two-tier bitmap correctness (refill/spill)
- Mini-magazine overflow/underflow
- Bitmap-magazine consistency

**Integration tests**:
- Existing bench_tiny benchmarks
- Multi-threaded stress tests
- Diagnostic feature validation

**Performance tests**:
- Before/after latency comparison
- Hit rate measurement (mini-mag vs refill)

**Estimated effort**: **6-8 hours** (implementation + testing)

---

## 6. Risks and Mitigation

### Risk 1: Mini-Magazine Size Tuning

**Problem**: Too small (8) → frequent refills; too large (64) → memory overhead

**Mitigation**:
- Make `mag_max` tunable via environment variable
- Adaptive sizing based on allocation pattern
- Start with 16-32 (sweet spot)

### Risk 2: Bitmap Refill Overhead

**Problem**: If mini-mag empties frequently, refill cost dominates

**Scenarios**:
- Burst allocation (1000 allocs in a row) → 1000/16 = 62 refills
- Refill cost: 62 * 48ns = 2976ns total = **3ns/alloc amortized** ✅

**Mitigation**: Batch size (16) amortizes cost well

### Risk 3: TLS Magazine Integration

**Problem**: Unclear how to integrate with existing TLS Magazine

**Options**:
1. Remove TLS Magazine entirely → **Simplest**
2. Keep TLS Magazine, add page mini-mag → **Complex**
3. Replace TLS Magazine with TLS mini-mag (64-128 items) → **Recommended**

**Mitigation**: Prototype Option 3, benchmark against current

### Risk 4: Diagnostic Lag

**Problem**: Bitmap doesn't reflect mini-mag state in real-time

**Scenarios**:
- Profiler reads bitmap → sees "free" but block is in mini-mag
- Fix: Flush before diagnostic read

**Mitigation**:
```c
void flush_diagnostics() {
    for_each_class(c) {
        spill_to_bitmap(g_tls_cache[c].active);
    }
}
```

---

## 7. Performance Comparison Matrix

| Approach | Fast Path | Research | Complexity | Risk | Improvement |
|----------|-----------|----------|------------|------|-------------|
| **Current (Bitmap only)** | 83 ns | ✅ Full | Low | Low | Baseline |
| **Strategy A (Bitmap + cleanup)** | 58-65 ns | ✅ Full | Low | Low | +25-30% |
| **Strategy B (Free-list only)** | 45-55 ns | ❌ Lost | Moderate | Moderate | +35-45% |
| **Hybrid (Bitmap+Mini-Mag)** | **35-45 ns** | ✅ Full | Moderate | Moderate | **45-58%** |

**Winner**: **Hybrid** (best speed + research preservation)

---

## 8. Recommended Implementation Plan

### Phase 1: Two-Tier Bitmap (2-3 hours)

**Goal**: Eliminate empty word scan overhead
```c
// Add bm_top to existing TinySlab
typedef struct TinySlab {
    uint64_t bm_top;      // NEW: Summary bitmap
    uint64_t bitmap[16];  // Existing
    // ...
} TinySlab;

// Update allocation to use bm_top
if (slab->bm_top == 0) return NULL;  // Fast empty check
int w = __builtin_ctzll(slab->bm_top);
// ...
```

**Expected**: 83ns → 78-80ns (+3-5ns)

**Risk**: Low (additive change)

### Phase 2: Page Mini-Magazine (3-4 hours)

**Goal**: Add LIFO mini-magazine to slabs
```c
typedef struct TinySlab {
    // Mini-magazine (NEW)
    Block* mag_head;
    uint16_t mag_count;
    uint16_t mag_max;  // 16

    // Two-tier bitmap (from Phase 1)
    uint64_t bm_top;
    uint64_t bitmap[16];
    // ...
} TinySlab;

void* tiny_alloc_fast() {
    Block* b = slab->mag_head;
    if (likely(b)) {
        slab->mag_head = b->next;
        return b;
    }
    // Refill from bitmap (batch of 16)
    refill_from_bitmap(slab, 16);
    // Retry
    return slab->mag_head ? pop_mag(slab) : NULL;
}
```

**Expected**: 78-80ns → 45-55ns (+25-35ns)

**Risk**: Moderate (structural change)

### Phase 3: TLS Integration (1-2 hours)

**Goal**: Integrate with existing TLS Magazine
```c
// Option: Replace TLS Magazine with TLS mini-mag
typedef struct TinyTLSCache {
    Block* mag_head;       // 64-128 items
    uint16_t mag_count;
    TinySlab* active;      // Current slab
    TinySlab* partial;     // Partial slabs
} TinyTLSCache;
```

**Expected**: 45-55ns → 35-45ns (+10ns from better TLS integration)

**Risk**: Moderate (requires careful testing)

### Phase 4: Statistics Batching (1 hour)

**Goal**: Remove per-allocation statistics overhead
```c
// Batch counter update (cold path only)
if (++g_tls_alloc_counter[class_idx] >= 100) {
    g_tiny_pool.alloc_count[class_idx] += 100;
    g_tls_alloc_counter[class_idx] = 0;
}
```

**Expected**: 35-45ns → 30-40ns (+5-10ns)

**Risk**: Low (independent change)

### Total Timeline

**Effort**: 7-10 hours
**Expected result**: 83ns → **30-45ns** (45-65% improvement)
**Research features**: ✅ Fully preserved (bitmap visibility maintained)

---

## 9. Comparison to Alternatives

### vs Strategy A (Bitmap + Cleanup)
- **Strategy A**: 83ns → 58-65ns (+25-30%)
- **Hybrid**: 83ns → 30-45ns (+45-65%)
- **Winner**: Hybrid (+20-30ns better)

### vs Strategy B (Free-list Only)
- **Strategy B**: 83ns → 45-55ns, ❌ loses research features
- **Hybrid**: 83ns → 30-45ns, ✅ keeps research features
- **Winner**: Hybrid (faster + research preserved)

### vs ChatGPT Pro's Estimate (55-60ns)
- **ChatGPT Pro**: 55-60ns (optimistic)
- **Realistic Hybrid**: 30-45ns (with all phases)
- **Conservative**: 40-50ns (if hit rate is lower)
- **Conclusion**: 55-60ns is achievable, 30-40ns is optimistic but possible

---

## 10. Conclusion

### Technical Verdict

**The Hybrid Bitmap+Mini-Magazine approach is sound and recommended** ✅

**Key strengths**:
1. ✅ Preserves bitmap visibility (research features intact)
2. ✅ Achieves free-list-like speed on hot path (30-45ns realistic)
3. ✅ Two-tier bitmap eliminates empty scan overhead
4. ✅ Well-established pattern (mimalloc uses similar techniques)

**Key concerns**:
1. ⚠️ Moderate implementation complexity (7-10 hours)
2. ⚠️ TLS Magazine integration needs careful design
3. ⚠️ Bitmap consistency requires flush for diagnostics
4. ⚠️ Performance depends on mini-magazine hit rate (90%+ needed)

### Recommendation

**Adopt the Hybrid approach with 4-phase implementation**:
1. Two-tier bitmap (low risk, immediate gain)
2. Page mini-magazine (moderate risk, big gain)
3. TLS integration (moderate risk, polish)
4. Statistics batching (low risk, final optimization)

**Expected outcome**: **83ns → 30-45ns** (45-65% improvement) while preserving all research features

### Next Steps

1. ✅ Create final implementation strategy document
2. ✅ Update TINY_POOL_OPTIMIZATION_STRATEGY.md to Hybrid approach
3. ✅ Begin Phase 1 (Two-tier bitmap) implementation
4. ✅ Validate with benchmarks after each phase

---

**Last Updated**: 2025-10-26
**Status**: Analysis complete, ready for implementation
**Confidence**: HIGH (backed by mimalloc precedent, realistic estimates)
**Risk Level**: MODERATE (phased approach mitigates risk)